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Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -1 to 1. The increments on the x-axis are marked in intervals of ½π.

Trigonometry Grid With Domain -4π to 4π And Range -1 to 1

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -1 to 1. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -1 to 1. The increments on the x-axis are marked in intervals of 1/3π.

Trigonometry Grid With Domain -4π to 4π And Range -1 to 1

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -1 to 1. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -10 to 10. The increments on the x-axis are marked in intervals of ½π.

Trigonometry Grid With Domain -4π to 4π And Range -10 to 10

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -10 to 10.…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -10 to 10. The increments on the x-axis are marked in intervals of 1/3π.

Trigonometry Grid With Domain -4π to 4π And Range -10 to 10

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -10 to 10.…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -10 to 10. The increments on the x-axis are marked in intervals of ¼π.

Trigonometry Grid With Domain -4π to 4π And Range -10 to 10

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -10 to 10.…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -2 to 2. The increments on the x-axis are marked in intervals of ½π.

Trigonometry Grid With Domain -4π to 4π And Range -2 to 2

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -2 to 2. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -2 to 2. The increments on the x-axis are marked in intervals of 1/3π.

Trigonometry Grid With Domain -4π to 4π And Range -2 to 2

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -2 to 2. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -2 to 2. The increments on the x-axis are marked in intervals of ¼π.

Trigonometry Grid With Domain -4π to 4π And Range -2 to 2

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -2 to 2. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -3 to 3. The increments on the x-axis are marked in intervals of ½π.

Trigonometry Grid With Domain -4π to 4π And Range -3 to 3

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -3 to 3. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -3 to 3. The increments on the x-axis are marked in intervals of 1/3π.

Trigonometry Grid With Domain -4π to 4π And Range -3 to 3

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -3 to 3. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -3 to 3. The increments on the x-axis are marked in intervals of ¼π.

Trigonometry Grid With Domain -4π to 4π And Range -3 to 3

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -3 to 3. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -4 to 4. The increments on the x-axis are marked in intervals of ½π.

Trigonometry Grid With Domain -4π to 4π And Range -4 to 4

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -4 to 4. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -4 to 4. The increments on the x-axis are marked in intervals of 1/3π.

Trigonometry Grid With Domain -4π to 4π And Range -4 to 4

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -4 to 4. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -4 to 4. The increments on the x-axis are marked in intervals of ¼π.

Trigonometry Grid With Domain -4π to 4π And Range -4 to 4

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -4 to 4. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -5 to 5. The increments on the x-axis are marked in intervals of ½π.

Trigonometry Grid With Domain -4π to 4π And Range -5 to 5

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -5 to 5. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -5 to 5. The increments on the x-axis are marked in intervals of 1/3π.

Trigonometry Grid With Domain -4π to 4π And Range -5 to 5

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -5 to 5. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -5 to 5. The increments on the x-axis are marked in intervals of ¼π.

Trigonometry Grid With Domain -4π to 4π And Range -5 to 5

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -5 to 5. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -6 to 6. The increments on the x-axis are marked in intervals of ½π.

Trigonometry Grid With Domain -4π to 4π And Range -6 to 6

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -6 to 6. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -6 to 6. The increments on the x-axis are marked in intervals of 1/3π.

Trigonometry Grid With Domain -4π to 4π And Range -6 to 6

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -6 to 6. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -6 to 6. The increments on the x-axis are marked in intervals of ¼π.

Trigonometry Grid With Domain -4π to 4π And Range -6 to 6

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -6 to 6. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -7 to 7. The increments on the x-axis are marked in intervals of ½π.

Trigonometry Grid With Domain -4π to 4π And Range -7 to 7

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -7 to 7. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -7 to 7. The increments on the x-axis are marked in intervals of 1/3π.

Trigonometry Grid With Domain -4π to 4π And Range -7 to 7

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -7 to 7. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -7 to 7. The increments on the x-axis are marked in intervals of ¼π.

Trigonometry Grid With Domain -4π to 4π And Range -7 to 7

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -7 to 7. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -8 to 8. The increments on the x-axis are marked in intervals of ½π.

Trigonometry Grid With Domain -4π to 4π And Range -8 to 8

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -8 to 8. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -8 to 8. The increments on the x-axis are marked in intervals of 1/3π.

Trigonometry Grid With Domain -4π to 4π And Range -8 to 8

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -8 to 8. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -8 to 8. The increments on the x-axis are marked in intervals of ¼π.

Trigonometry Grid With Domain -4π to 4π And Range -8 to 8

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -8 to 8. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -9 to 9. The increments on the x-axis are marked in intervals of ½π.

Trigonometry Grid With Domain -4π to 4π And Range -9 to 9

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -9 to 9. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -9 to 9. The increments on the x-axis are marked in intervals of 1/3π.

Trigonometry Grid With Domain -4π to 4π And Range -9 to 9

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -9 to 9. The…

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -9 to 9. The increments on the x-axis are marked in intervals of ¼π.

Trigonometry Grid With Domain -4π to 4π And Range -9 to 9

Illustration of a trigonometric grid with a domain from -4π to 4π and a range from -9 to 9. The…

Illustration that can be used to show that when given an angle, expressed as an inverse function of u, it can be used to find the value of any function of the angle in terms of u.

Angle Expressed As An Inverse Function

Illustration that can be used to show that when given an angle, expressed as an inverse function of…

A perpendicular line drawn from point P to straight line RS.

Perpendicular Line Drawn From Point P to Line RS

A perpendicular line drawn from point P to straight line RS.

CD is the projection of AB upon OX. In each case AE=CD and AE=ABcos theta.

Projection of a Line Segment

CD is the projection of AB upon OX. In each case AE=CD and AE=ABcos theta.

Illustration of an angle &alpha with the vertex at the center, O, of a circle with radius OB. AC and BD are perpendicular to OB and join B with C. The are of the triangle OBC is less than the are of the sector OBC, and the sector OBC is less than the triangle OBD.

Triangles and Sectors in Quadrant I

Illustration of an angle &alpha with the vertex at the center, O, of a circle with radius OB. AC and…

Illustration of an angle &alpha with the terminal side used to draw a triangle in quadrant I.

Triangle in Quadrant I

Illustration of an angle &alpha with the terminal side used to draw a triangle in quadrant I.

Illustration of an angle with the terminal side used to draw a triangle in quadrant II.

Triangle in Quadrant II

Illustration of an angle with the terminal side used to draw a triangle in quadrant II.

Roof with a slope of 30 degrees. Angle theta is the inclination to the horizontal of the line AB, drawn in the roof and making an angle of 35 degrees with the line of greatest slope.

Roof With 30 degree Inclination for Trigonometry Triangle Problems

Roof with a slope of 30 degrees. Angle theta is the inclination to the horizontal of the line AB, drawn…

Secant and Cosecant curves plotted from negative pi to 2 pi. Graph of y=sec x and y=csc x.

Secant and Cosecant Curves, y=sec x and y=csc x

Secant and Cosecant curves plotted from negative pi to 2 pi. Graph of y=sec x and y=csc x.

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center of a circle through one extremity of an arc (whose secant it is said to be) to the tangent from the other extremity of the same arc; or the ratio of this line to the radius; the reciprocal of the cosine. The ratio of AB to AD is the secant of the angle A; and AB is the secant of the arc CD." —Whitney, 1889

Circle with Secant

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center…

The sector is a hinged rule with scales used for various mathematical calculations.

Sector

The sector is a hinged rule with scales used for various mathematical calculations.

Sine curve plotted from 0 to 2 pi. Graph of y=sin x.

Sine Curve y=sin x

Sine curve plotted from 0 to 2 pi. Graph of y=sin x.

Sine curves of varying frequency and amplitude plotted from 0 to 2 pi. Graph of y= sin θ, y= 1/2 sin θ, y=2 sin θ, y= 2 sin 3θ

Sine Curves y= sin Ǝ, y= 1/2 sin Ǝ, y=2 sin Ǝ, y= 2 sin 3Ǝ

Sine curves of varying frequency and amplitude plotted from 0 to 2 pi. Graph of y= sin θ, y= 1/2…

Sine curves of varying frequency plotted from 0 to 2 pi. Graph of y= sin t, y= r sin1/2t, y=r sin 2t.

Sine Curves y= sin t, y= r sin1/2t, y= r sin 2t

Sine curves of varying frequency plotted from 0 to 2 pi. Graph of y= sin t, y= r sin1/2t, y=r sin 2t.

The curve of a sine wave.

Curves of sines

The curve of a sine wave.

Illustration two types of triangles that can be used to model the law of sines. "In a plane triangle any two sides are to each other as the sines of the opposite angles."

Law of Sines

Illustration two types of triangles that can be used to model the law of sines. "In a plane triangle…

Illustration of a right spherical triangle and the five circular parts placed in the sectors of a circle in the order in which they occur in the triangle. "The ten formulas used in the solution of spherical right triangles can be expressed by means of two rules, known as Napier's rules of circular parts."

Napier's Right Spherical Triangle

Illustration of a right spherical triangle and the five circular parts placed in the sectors of a circle…

Illustration used, with the law of sines, to find the relation between two sides of a spherical triangle and the angles opposite.

Relationships In A Spherical Triangle

Illustration used, with the law of sines, to find the relation between two sides of a spherical triangle…

Illustration used, with the law of cosines, to find the relation between the three sides and an angle of a spherical triangle.

Relationships In A Spherical Triangle

Illustration used, with the law of cosines, to find the relation between the three sides and an angle…

Illustration used to extend the law of cosines when finding the relation between the three sides and an angle of a spherical triangle. In this case both angles b and c are greater than 90°.

Relationships In A Spherical Triangle

Illustration used to extend the law of cosines when finding the relation between the three sides and…

Illustration used to extend the law of cosines when finding the relation between the three sides and an angle of a spherical triangle. In this case angle b<90&deg; and angle c>90&deg;.

Relationships In A Spherical Triangle

Illustration used to extend the law of cosines when finding the relation between the three sides and…

Illustration of a right spherical triangle with a and b the sides, and &alpha; and &beta; the angles opposite them. Side c is the hypotenuse.

Right Spherical Triangle

Illustration of a right spherical triangle with a and b the sides, and α and β the angles…

Illustration of spiral with unequally spaced intervals.

Spiral

Illustration of spiral with unequally spaced intervals.

Illustration of spiral.

Spiral

Illustration of spiral.

Illustration of spiral with unequally spaced intervals.

Spiral

Illustration of spiral with unequally spaced intervals.

Illustration of spiral with unequally spaced intervals.

Spiral

Illustration of spiral with unequally spaced intervals.

Illustration of spiral.

Spiral

Illustration of spiral.

Illustration of spiral with unequally spaced intervals.

Spiral

Illustration of spiral with unequally spaced intervals.

Illustration of spiral with unequally spaced intervals.

Spiral

Illustration of spiral with unequally spaced intervals.

Illustration of spiral with unequally spaced intervals.

Spiral

Illustration of spiral with unequally spaced intervals.

Two set squares, whose sides are 3,4, and 5 in., are placed so that their 4-in. sides and right angles coincide, and the angle between the 3-in. sides is 50 degrees. Theta, &#398; is the angle between the longest sides.

Two Squares With Sides of Lengths 3,4,5 Placed at Right Angles to Each Other

Two set squares, whose sides are 3,4, and 5 in., are placed so that their 4-in. sides and right angles…

Illustration of a giant stepladder, sometimes called a skyscraper stepladder, that is opened next to a palm tree. One of the bottom legs of the unfolded ladder is adjacent to the tree. The ladder forms an isosceles triangle with the ground.

Skyscraper Giant Stepladder

Illustration of a giant stepladder, sometimes called a skyscraper stepladder, that is opened next to…