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. 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. 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 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. 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. 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. 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. 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 showing a circle with various chords and tangents drawn.

Circle With Various Chords And Tangents

Illustration showing a circle with various chords and tangents drawn.

Illustration showing a circle with various chords and tangents drawn.

Circle With Various Chords And Tangents

Illustration showing a circle with various chords and tangents drawn.

Illustration where one leg of a right triangle is the diameter of a circle. The tangent at the point where the circumference cuts the hypotenuse bisects the other leg.

Circle With a Right Triangle

Illustration where one leg of a right triangle is the diameter of a circle. The tangent at the point…

Illustration showing that from any point in the circumference of a circle, a chord and a tangent are drawn, the perpendiculars dropped on them from the middle point of the subtended arc are equal.

Circle With a Tangent Line and Chord

Illustration showing that from any point in the circumference of a circle, a chord and a tangent are…

2 congruent circles whose intersection includes a tangent circle with diameter equal to the radii of the larger circles.

2 Intersecting Circles

2 congruent circles whose intersection includes a tangent circle with diameter equal to the radii of…

A large circle containing 3 smaller congruent circles. The small circles are externally tangent to each other and internally tangent to the larger circle.

3 Smaller Circles In A Larger Circle

A large circle containing 3 smaller congruent circles. The small circles are externally tangent to each…

A large circle containing 3 smaller congruent circles. The small circles are externally tangent to each other and internally tangent to the larger circle.

3 Smaller Circles In A Larger Circle

A large circle containing 3 smaller congruent circles. The small circles are externally tangent to each…

A large circle containing 4 smaller congruent circles. The small circles are externally tangent to each other and internally tangent to the larger circle.

4 Smaller Circles In A Larger Circle

A large circle containing 4 smaller congruent circles. The small circles are externally tangent to each…

A large circle containing 4 smaller congruent circles. The small circles are externally tangent to each other and internally tangent to the larger circle.

4 Smaller Circles In A Larger Circle

A large circle containing 4 smaller congruent circles. The small circles are externally tangent to each…

A sequence of five circles tangent to each other at a point. The radius decreases by one half in each successive circle.

5 Tangent Circles

A sequence of five circles tangent to each other at a point. The radius decreases by one half in each…

A regular hexagon containing 7 congruent circles. The circles are externally tangent to each other and internally tangent to the hexagon.

7 Congruent Circles In A Regular Hexagon

A regular hexagon containing 7 congruent circles. The circles are externally tangent to each other and…

A large circle containing 7 smaller congruent circles. The small circles are externally tangent to each other and internally tangent to the larger circle.

7 Smaller Circles In A Larger

A large circle containing 7 smaller congruent circles. The small circles are externally tangent to each…

A large circle containing 7 smaller congruent circles. The small circles are externally tangent to each other and internally tangent to the larger circle.

7 Smaller Circles In A Larger Circle

A large circle containing 7 smaller congruent circles. The small circles are externally tangent to each…

7 congruent circles. 6 of the circles are equally placed about the center circle. The circles are externally tangent to each other.

7 Tangent Circles

7 congruent circles. 6 of the circles are equally placed about the center circle. The circles are externally…

Illustration showing angles formed by two secants, two tangents, or a tangent and a secant, drawn to a circle form an external point. The angle is measured by half the difference of the intercepted arcs.

Circles With Angles Formed by Secants and Tangents

Illustration showing angles formed by two secants, two tangents, or a tangent and a secant, drawn to…

An illustration depicting an infinite sequence of tangent circles with the radius converging to zero. This is often called a Hawaiian earring.

Infinite Tangent Circles

An illustration depicting an infinite sequence of tangent circles with the radius converging to zero.…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated and rotated 45° to create the star-like illustration in scribed in the circle.

Reflected Arcs Of 2 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated and rotated 45° to create the star-like illustration.

Reflected Arcs Of 2 Circles

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of…

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated and rotated 45° and the overlapping curves are removed to create the star-like illustration.

Reflected Arcs Of 2 Circles

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of four times) and rotated 22.5° to create the star-like illustration in scribed in the circle.

Reflected Arcs Of 4 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of four times) and rotated 22.5° to create the star-like illustration.

Reflected Arcs Of 4 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of eight times) and rotated 11.25° to create the star-like illustration in scribed in the circle.

Reflected Arcs Of 8 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of eight times) and rotated 11.25° to create the star-like illustration.

Reflected Arcs Of 8 Circles

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

Illustration of a 6-point star (convex dodecagon) inscribed in a large circle and circumscribed about a smaller circle.

Star Inscribed And Circumscribed About Circles

Illustration of a 6-point star (convex dodecagon) inscribed in a large circle and circumscribed about…

Illustration of an 8-point star (convex polygon) inscribed in a large circle and circumscribed about a smaller circle.

Star Inscribed And Circumscribed About Circles

Illustration of an 8-point star (convex polygon) inscribed in a large circle and circumscribed about…

Illustration showing 2 circles with that touch each other and two lines drawn through the point of contact terminated by the circumference. The chords joining the ends of theses lines are parallel.

Tangent Circles With Chords

Illustration showing 2 circles with that touch each other and two lines drawn through the point of contact…

The lines which join corresponding points in an involution on a conic all pass through a fixed point; and reciprocally, the points of intersection of conjugate lines in an involution among tangents to a conic lie on a line.

Conic Involution

The lines which join corresponding points in an involution on a conic all pass through a fixed point;…

Illustration that can be used to show that if the cotangent of an angle is negative the angle must terminate in either the second or fourth quadrant.

Negative Cotangent Angles

Illustration that can be used to show that if the cotangent of an angle is negative the angle must terminate…

Illustration of 108 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

108 Stacked Congruent Cubes

Illustration of 108 congruent cubes stacked at various heights. A 3-dimensional representation on a…

Illustration of 117 congruent cubes stacked in columns of one, four, and six. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

117 Stacked Congruent Cubes

Illustration of 117 congruent cubes stacked in columns of one, four, and six. A 3-dimensional representation…

Illustration of 128 congruent cubes stacked so they form a rectangular solid that measures 4 by 4 by 8. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

128 Stacked Congruent Cubes

Illustration of 128 congruent cubes stacked so they form a rectangular solid that measures 4 by 4 by…

Illustration of 132 congruent cubes stacked in 22 columns of 6 in the shape of a U. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

132 Stacked Congruent Cubes

Illustration of 132 congruent cubes stacked in 22 columns of 6 in the shape of a U. A 3-dimensional…

Illustration of 154 congruent cubes stacked in columns increasing from one to four. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

154 Stacked Congruent Cubes

Illustration of 154 congruent cubes stacked in columns increasing from one to four. A 3-dimensional…

Illustration of 16 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

16 Stacked Congruent Cubes

Illustration of 16 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

Illustration of 17 congruent cubes stacked in ones and twos in the shape of a V. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

17 Stacked Congruent Cubes

Illustration of 17 congruent cubes stacked in ones and twos in the shape of a V. A 3-dimensional representation…

Illustration of two congruent cubes that are tangent along an edge. A 3-dimensional representation on a 2-dimensional surface.

2 Congruent Cubes

Illustration of two congruent cubes that are tangent along an edge. A 3-dimensional representation on…

Illustration of 20 congruent cubes stacked in twos and threes. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

20 Stacked Congruent Cubes

Illustration of 20 congruent cubes stacked in twos and threes. A 3-dimensional representation on a 2-dimensional…

Illustration of 20 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

20 Stacked Congruent Cubes

Illustration of 20 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

Illustration of 20 congruent cubes stacked at heights increasing from 1 to 4 cubes. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

20 Stacked Congruent Cubes

Illustration of 20 congruent cubes stacked at heights increasing from 1 to 4 cubes. A 3-dimensional…

Illustration of 22 congruent cubes stacked in ones, twos, and threes. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

22 Stacked Congruent Cubes

Illustration of 22 congruent cubes stacked in ones, twos, and threes. A 3-dimensional representation…

Illustration of 22 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

22 Stacked Congruent Cubes

Illustration of 22 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…

Illustration of 24 congruent cubes stacked at various heights to resemble steps. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

24 Stacked Congruent Cubes

Illustration of 24 congruent cubes stacked at various heights to resemble steps. A 3-dimensional representation…

Illustration of 256 congruent cubes stacked so they form 4 larger cubes that measures 4 by 4 by 4 each. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

256 Stacked Congruent Cubes

Illustration of 256 congruent cubes stacked so they form 4 larger cubes that measures 4 by 4 by 4 each.…

Illustration of 27 congruent cubes stacked to resemble a larger cube that measures three by three by three cubes. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

27 Stacked Congruent Cubes

Illustration of 27 congruent cubes stacked to resemble a larger cube that measures three by three by…

Illustration of 27 congruent cubes stacked at various heights in the shape of a W. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

27 Stacked Congruent Cubes

Illustration of 27 congruent cubes stacked at various heights in the shape of a W. A 3-dimensional representation…

Illustration of 28 congruent cubes placed in the shape of a square. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

28 Congruent Cubes Placed in the Shape of a Square

Illustration of 28 congruent cubes placed in the shape of a square. A 3-dimensional representation on…

Illustration of 30 congruent cubes stacked in decreasing heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

30 Stacked Congruent Cubes

Illustration of 30 congruent cubes stacked in decreasing heights. A 3-dimensional representation on…

Illustration of 33 congruent cubes stacked at various heights in a zigzag pattern. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

33 Stacked Congruent Cubes

Illustration of 33 congruent cubes stacked at various heights in a zigzag pattern. A 3-dimensional representation…

Illustration of 35 congruent cubes stacked in ones and twos in the shape of a W. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

35 Stacked Congruent Cubes

Illustration of 35 congruent cubes stacked in ones and twos in the shape of a W. A 3-dimensional representation…

Illustration of 35 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional surface that can be used for testing depth perception and identifying and counting cubes, edges, and faces.

35 Stacked Congruent Cubes

Illustration of 35 congruent cubes stacked at various heights. A 3-dimensional representation on a 2-dimensional…