ClipArt ETC
Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. The circle is marked and labeled in radians. All quadrantal angles and angles that have reference angles of 30°, 45°, and 60° are given in radian measure in terms of pi. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Special Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. All quadrantal angles and angles that have reference angles of 30°, 45°, and 60° are given in radian measure in terms of pi. At each quadrantal angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled At Special Angles

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. All quadrantal angles and angles that have reference angles of 30°, 45°, and 60° are given in radian measure in terms of pi.

Unit Circle Labeled At Special Angles

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. All quadrantal angles and angles that have reference angles of 30°, 45°, and 60° are marked from the origin, but no values are given.

Unit Circle Marked At Special Angles

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. All…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. All quadrantal angles are given in radian measure in terms of pi.

Unit Circle Labeled At Quadrantal Angles

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. All quadrantal angles are given in radian measure in terms of pi. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Quadrantal Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. All…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. At each quadrantal angle, the coordinates are given, but not the angle measure. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Quadrantal Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane. At each…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. At each quadrantal angle, the coordinates are given, but not the angle measure. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Quadrantal Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. All quadrantal angles are given in degree measure. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Quadrantal Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. All quadrantal angles are given in both radian and degree measure. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Quadrantal Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. At 45° increments, the angles are given in both radian and degree measure. At each quadrantal angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled In 45° Increments With Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. At 45° increments, the angles are given in both radian and degree measure. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled In 45° Increments With Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. The circle is marked and labeled in both radians and degrees at all quadrantal angles and angles that have reference angles of 30°, 45°, and 60°. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Special Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. The circle is marked and labeled in both radians and degrees at all quadrantal angles and angles that have reference angles of 30°, 45°, and 60°. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled With Special Angles And Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with the x- and y-axes indicated. At 30° increments, the angles are given in both radian and degree measure. At each angle, the coordinates are given. These coordinates can be used to find the six trigonometric values/ratios. The x-coordinate is the value of cosine at the given angle and the y-coordinate is the value of sine. From those ratios, the other 4 trigonometric values can be calculated.

Unit Circle Labeled In 30° Increments With Values

Illustration of a unit circle (circle with a radius of 1) superimposed on the coordinate plane with…

A section across the forearm a short distance below the elbow-joint. R and U, its two supporting bones, the radius and ulna; e, the epidermis, and d, the dermis of the skin; the latter is continuous below with bands of connective tissue, s, which penetrate between and invest the muscles, which are indicated by numbers; n, n, nerves and vessels.

Forearm, Section of

A section across the forearm a short distance below the elbow-joint. R and U, its two supporting bones,…

Bones of the arm. Labels: A, arm in supination; B, arm in pronation. H, humerus; R, radius; U, ulna.

Bones of the Arm

Bones of the arm. Labels: A, arm in supination; B, arm in pronation. H, humerus; R, radius; U, ulna.

Bow compasses should be used on all arcs and circles having a radius of less than 3/4 inch.

Bow Pencil

Bow compasses should be used on all arcs and circles having a radius of less than 3/4 inch.

Bow compasses should be used on all arcs and circles having a radius of less than 3/4 inch.

Bow Pen

Bow compasses should be used on all arcs and circles having a radius of less than 3/4 inch.

Bow compasses should be used on all arcs and circles having a radius of less than 3/4 inch.

Bow Divider

Bow compasses should be used on all arcs and circles having a radius of less than 3/4 inch.

For larger circles beam compasses are used. The two parts called channels which carry the pen and the needle point are clamped to a wooden beam at a distance equal to the radius of the circle. The thumb nut underneath one of the channel pieces makes accurate adjustment possible.

Beam Compasses

For larger circles beam compasses are used. The two parts called channels which carry the pen and the…

Circle pattern exercise: Draw diagonals A C and D B, and with the T-square draw the line E H. Now mark off on E H distances of 1.4 inch, and with H as a center describe, by means of the compasses, circles having radii respectively 2 inches, 1.5 inches, 1 inch, 0.75 inch, 0.5 inch, and .25 inch. Similarly with H as a center and a radius of 1.75 inch and 1.25 inches respectively raw the arcs F G and I J and K L and M N, being careful to end the arcs in the diagonals.

Circle Exercise

Circle pattern exercise: Draw diagonals A C and D B, and with the T-square draw the line E H. Now mark…

Arteries of the palm of the head and front of the forearm. Labels: 3, deep part of the raised pronator of the radius; 4, long supinator muscle; 5, long flexor of the thumb; 6, square pronator; 7, deep flexor of the fingers; 8, cubital flexor of the wrist; 9, annular ligament; 10, the brachial artery; 12, radial artery; 13, recurring radial artery joining the end of the upper deep one; 4, superficial veins; 15, cubital artery; 16, superficial palmary arch; 17, magna artery of the thumb and radial artery of the index; 18, back cubital recurring artery; 19, front interosseous artery; 20, back interosseous artery.

Arteries of the Hand and Forearm

Arteries of the palm of the head and front of the forearm. Labels: 3, deep part of the raised pronator…

In changing the compass from a small to large radius, hold the legs together with one hand and spin the nut with the other, in order to save wear on the threads.

Adjusting the Compass

In changing the compass from a small to large radius, hold the legs together with one hand and spin…

The radius, a bone of the arm.

Radius

The radius, a bone of the arm.

"Fore and Hind Leg of a Tapir. A, scapula; I, ilium, or shinbone of pelvis; H, humerus; F, femur; O, olecranon, or tip of the elbow; P, patella; U, ulna; T, tibia; R, radius; Fi, fibula." -Cooper, 1887

Tapir Legs

"Fore and Hind Leg of a Tapir. A, scapula; I, ilium, or shinbone of pelvis; H, humerus; F, femur; O,…

This figure shows "the cotidal lines and lines of equal amplitude for a diurnal tide in a circular sea of 20 degrees radius, the latitude of the center being 30 degrees north." -Coast and Geodetic Survey, 1901

Diurnal Cotidal Lines

This figure shows "the cotidal lines and lines of equal amplitude for a diurnal tide in a circular sea…

This figure shows "the cotidal lines and lines of equal amplitude for a diurnal tide in a circular sea of 20 degrees radius, the latitude of the center being 30 degrees north." -Coast and Geodetic Survey, 1901

Diurnal Cotidal Lines

This figure shows "the cotidal lines and lines of equal amplitude for a diurnal tide in a circular sea…

"Ideal fore limb. H., Humerus; R., radius; U., ulna; r'., radiale; u'., ulnare; i., intermedium; c., centrale; 1-5, carpalia bearing the corresponding digits with metacarpals (mc.) and phalanges (ph)." -Thomson, 1916

Vertebrate Fore Limb

"Ideal fore limb. H., Humerus; R., radius; U., ulna; r'., radiale; u'., ulnare; i., intermedium; c.,…

"Fore-limb and hind-limb compared. H., Humerus; R., radius; U., ulna; r., radiale; u., ulnare; C., distal carpals united to carpo-metacarpus; CC., the whole carpal region; MC.I., metacarpal of the thumb; I., phalanx of the thumb; MC.II., second metacarpus; II., second digit; MC.III., third metacarpus; III., third digit. F., femur; T.T., tibio-tarsus; Fi., fibula; Pt., proximal tarsals united to lower end of tibia; dt., distal tarsals nited to upper end of tarso-metatarsus (T.MT.); T., entire tarsal region; MT.I., first metatarsal, free; I.-IV., toes." -Thomson, 1916

Bird Limbs

"Fore-limb and hind-limb compared. H., Humerus; R., radius; U., ulna; r., radiale; u., ulnare; C., distal…

"Wing of dove. h., Humerus; s.f., secondary feathers; r., radius; u., ulna; c., carpals; mc., carpo-metacarpus; p.f., primary feathers." -Thomson, 1916

Dove Wing

"Wing of dove. h., Humerus; s.f., secondary feathers; r., radius; u., ulna; c., carpals; mc., carpo-metacarpus;…

"Fore-limb and shoulder-girdle (I.) and hind-limb (II.) of rabbit. SC., Scapula; A., acromion; M., metacromion process; H., humerus; O., olecranon process; U., ulna; R., radius; C., carpals; MC., metacarpals; D., five digits; F., femur; P., patella; FI., fibula; T., tibia; OC., os calcis; AS., astragalus; DT., distal tarsals; MT., metatarsals; D., four digits." -Thomson, 1916

Rabbit Limbs

"Fore-limb and shoulder-girdle (I.) and hind-limb (II.) of rabbit. SC., Scapula; A., acromion; M., metacromion…

"Left fore-limb of Balaenoptera. Sc., Sca pula with spine (sp.); H., humerus; R., radius; U., ulna; C., carpals embedded in matrix; Mc., metacarpals; Ph., phalanges." -Thomson, 1916

Whale Forelimb

"Left fore-limb of Balaenoptera. Sc., Sca pula with spine (sp.); H., humerus; R., radius; U., ulna;…

"Skeleton of male gorilla. cl., Clavicle; sc., tip of scapula; S., praesternum; H., humerus; r., radius; u., ulna; Il., ilium; C., coccyx; P., pubis; Is., ischium; F., femur; t., tibia; f., fibula." -Thomson, 1916

Gorilla Skeleton

"Skeleton of male gorilla. cl., Clavicle; sc., tip of scapula; S., praesternum; H., humerus; r., radius;…

Illustration showing a circle with a radius of 2 in. intersecting a circle with a radius of 3 in..

2 Intersecting Circles

Illustration showing a circle with a radius of 2 in. intersecting a circle with a radius of 3 in..

"A circle may be considered as made up of triangles whose bases form the circumference, and whose altitude is the radius (1/2 diameter) of the circle." This is clearly shown by the cut at the left.

Circle Made Up Of Triangles

"A circle may be considered as made up of triangles whose bases form the circumference, and whose altitude…

"Diagrams of the girdles and appendages in a typical Vertebrate. A, anterior; B, posterior. ac., acetabulum, articulation of the humerus with its girdle; c, coracoid; ca., carpals; c.e., centralia; d.c., distal carpals; d.t., distal tarsals; el., elbow joint; f, fibula; fe., femur; fi., fibulare; gc., glenoid cavity, articulation of arm with girdle; h, humerus; il., ilium; in., intermediale; is. ischium; kn., knee joint; m.c., metacarpals (1-5); m.t., metatarsals (1-5); p, pubis; ph., phalanges (1-5); pr.c., precoracoid; r, radius; ra., radiale; sc., scapula; t, tibia; ta., tarsals; ti., tibiale; u., ulna; ul., ulnare." -Galloway, 1915

Vertebrate Appendages

"Diagrams of the girdles and appendages in a typical Vertebrate. A, anterior; B, posterior. ac., acetabulum,…

"Skeleton of crocodile. C, causal region; D, thoracic region of spinal column; F, fibula; Fe, femur; H, humerus; I, ischium; L, lumbar region; R, radius; Ri, ribs; S, sacrum; Sc, scapula; Sta, abdominal ribs; T, tibia; U, ulna." -Parker, 1900

Crocodile Skeleton

"Skeleton of crocodile. C, causal region; D, thoracic region of spinal column; F, fibula; Fe, femur;…

"Cistudo lutaria. Skeleton seen from below; the plastron has been removed and is represented on one side. C, costal plate; Co, coracoid; e, entoplastron; Ep, epiplastron; F, fibula; Fe, femur; H, humerus; Il, ilium; Is, ischium; M, marginal plates; Nu, nuchal plate; Pb, pubis; Pro, pro-coracoid; Py, pygal plates; R, radius; Sc, scapula; T, tibia; U, ulna." -Parker, 1900

Marsh Turtle Skeleton

"Cistudo lutaria. Skeleton seen from below; the plastron has been removed and is represented on one…

"Columba livia. Left manus of a nestling. The cartilaginous parts are dotted. cp. 1, radiale; cp. 2, ulnare; mcp. 1, 2, 3, metacarpals; ph. 1, phalanx of first digit; ph. 2, ph. 2', phalanges of second digit; ph. 3, phalanx of third digit; ra, radius; ul, ulna." -Parker, 1900

Rock Pigeon Manus

"Columba livia. Left manus of a nestling. The cartilaginous parts are dotted. cp. 1, radiale; cp. 2,…

Biceps muscle attached to the radius.

Biceps Muscle and Radius

Biceps muscle attached to the radius.

A circle with labels for radius, diameter, and circumference. The visual will help to remember what each term means.

Circle Parts

A circle with labels for radius, diameter, and circumference. The visual will help to remember what…

An illustration showing the construction used to divide a line AB into two equal parts; and to erect a perpendicular through the middle. "With the end A and B as centers, draw the dotted circle arcs with a radius greater than half the line. Through the crossings of the arcs draw the perpendicular CD, which divides the line into two equal parts."

Construction Of A Line Divided In Equal Parts

An illustration showing the construction used to divide a line AB into two equal parts; and to erect…

An illustration showing the construction used to erect a perpendicular at the end of a line. "With the point D as a center at a distance from the line, and with AD as radius, draw the dotted circle arc so that it cuts the line at E through E and D, draw the diameter EC: then join C and A, which will be the required perpendicular."

Construction Of A Perpendicular

An illustration showing the construction used to erect a perpendicular at the end of a line. "With the…

An illustration showing the construction used to erect a parallel line. "With C as a center, draw the dotted arc ED, with E as a center, draw through C the dotted arc F.C. With the radius FC and E as a center, draw the cross arc at D. Join C with the cross at D, which will be the required parallel line.

Construction Of A Parallel

An illustration showing the construction used to erect a parallel line. "With C as a center, draw the…

An illustration showing the construction used to erect an equal angle. "With D as a center, draw the dotted arc CE: and with the same radius and B as a center, draw the arc GF; then make GF equal to CE; then join BF, which will form the required angle, FBG=CDE."

Construction Of An Equal Angle

An illustration showing the construction used to erect an equal angle. "With D as a center, draw the…

An illustration showing how to find the center of a circle which will pass through three given points A, B, and C. "With B as a center, draw the arc DEFG; and with the same radius and A as a center, draw the cross arcs D and F; also with C as a center, draw the cross arcs E and G. Join D and F, and also E and G, and the crossing o is the required center of the circle."

Find The Center Of A Circle Through 3 Points

An illustration showing how to find the center of a circle which will pass through three given points…

An illustration showing how to construct a square upon a given line. "With AB as radius and A and B as centers, draw the circle arcs AED and BEC. Divide the arc BE in two equal parts at F, and with EF as radius and E as center, draw the circle CFD. Join A and CB and D, C and D, which completes the required square."

Square Constructed Upon A Given Line

An illustration showing how to construct a square upon a given line. "With AB as radius and A and B…

An illustration showing how to construct a tangent circle to a circle with a given radius. "Through the given point C, draw the diameter AC extended beyond D: from C set off the given radius R to D; then D is the center of the required circle, which tangents the given circle at C."

Construction Of Circle Tangent To Circle

An illustration showing how to construct a tangent circle to a circle with a given radius. "Through…

An illustration showing how to construct a tangent to 2 given circles of different diameters. "Join the centers C and c of the given circles, and extend the line to D; draw the radii AC and ac parallel with one another. Join Aa, and extend the line to D. On CD as a diameter, draw the half circle CeD; on cD as a diameter, draw the half circle cfD; then the crossings e and f are the tangenting points of the circles."

Construction Of Tangent To 2 Circles

An illustration showing how to construct a tangent to 2 given circles of different diameters. "Join…

An illustration showing how to construct a circle tangent to a given line and given circle. "Add the given radius r to the radius R of the circle, and draw the arc cd. Draw the line ce parallel with and at a distance r from the line AB. Then the crossing c is the center of the required circle that will tangent the given line and circle."

Construction Of A Circle Tangent To A Line And A Circle

An illustration showing how to construct a circle tangent to a given line and given circle. "Add the…

An illustration showing how to construct the center and radius of a circle that will tangent a given circle. "Through the given point C, draw the tangent GF; bisect the angle FGE; then o is the center of the required circle that will tangent AB at C, and the line DE."

Construction Of A Center And Radius Of A Circle That Will Tangent A Given Circle

An illustration showing how to construct the center and radius of a circle that will tangent a given…

An illustration showing how to construct the center and radius of a circle that will tangent a given circle and line. "Through the given point C, draw the line EF at right angles to AB; set off from C the radius r of the given circle. Join G and F. With G and F as centers draw the arc crosses m and n. Join mn, and where it crosses the line EF is the center of the required circle."

Construction Of A Center And Radius Of A Circle That Will Tangent A Given Circle And Line

An illustration showing how to construct the center and radius of a circle that will tangent a given…

An illustration showing how to construct the center and radius of a circle that will tangent a given circle and line. "From C, erect the perpendicular CG; set off the given radius r from C to H. With H as a center and r as radius, draw the cross arcs on the circle. Through the cross arcs draw the line IG; then G is the center of the circle arc FIC, which tangents the line at C and the circle at F."

Construction Of A Center And Radius Of A Circle That Will Tangent A Given Circle And Line

An illustration showing how to construct the center and radius of a circle that will tangent a given…

An illustration showing how to construct two circles that tangent themselves and two given lines. "Draw the center line AB between the given lines; assume D to be the tangenting point of the circles; draw DC at right angles to AB. With C as center and CD as radius, draw the circle EDF. From E, draw Em at right angles to EF; and from F draw Fm at right angles to FE; then m and n are the centers for the required circles."

Construction Of Two Circles That Tangent Themselves and 2 Given Lines

An illustration showing how to construct two circles that tangent themselves and two given lines. "Draw…

An illustration showing how to construct a circle that tangents two given lines inclined to one another with the one tangenting point being given. "Draw the center line GF. From E, draw EF at right angles to AB; then F is the center of the circle required.

Construction Of A Circle That Tangents 2 Given Lines

An illustration showing how to construct a circle that tangents two given lines inclined to one another…

An illustration showing how to construct a circle that tangents two given lines and goes through a given point c on the line FC, which bisects the angle of the lines. "Through C draw AB at right angles to CF; bisect the angles DAB and EBA, and the crossing on CF is the center of the required circle."

Construction Of A Circle That Tangents 2 Given Lines And Goes Through A Given Point

An illustration showing how to construct a circle that tangents two given lines and goes through a given…

An illustration showing how to construct a circle arc without recourse to its center, but its chord AB and height h being given. "With the chord as radius, and A and B as centers, draw the dotted circle arcs AC and BD. Through the point O draw the lines AOo and BOo. Make the arcs Co=Ao and Do=Bo. Divide these arcs into any desired number of equal parts, and number them as shown on the illustration. Join A and B with the divisions, and the crossings of equal numbers are points in the circle arc."

Construction Of A Circle Arc

An illustration showing how to construct a circle arc without recourse to its center, but its chord…

An illustration showing how to construct a center and radius of a circle that will tangent the three sides of a triangle. "Bisect two of the angles in the triangle, and the crossing C is the center of the required circle."

Construction Of The Center And Radius Of A Circle Tangent To Triangle Sides

An illustration showing how to construct a center and radius of a circle that will tangent the three…

An illustration showing how to construct an equilateral triangle inscribed in a circle. "With the radius of the circle and center C draw the arc DFE; with the same radius, and D and E as centers, set off the points A and B. Join A and B, B and C, C and A, which will be the required triangle."

Construction Of An Equilateral Triangle Inscribed In A Circle

An illustration showing how to construct an equilateral triangle inscribed in a circle. "With the radius…