The Unit Circle and Trigonometric Functions

The coordinate point on the unit circle at angle -135º.

(-√2/2, -√2/2)

The coordinate point on the unit circle at angle 3π/4.

(-√2/2, √2/2)

The coordinate point on the unit circle at angle 210º.

(-√3/2, -1/2)

The coordinate point on the unit circle at angle 150º.

(-√3/2, 1/2)

The coordinate point on the unit circle at angle -270º.

(0, 1)

The coordinate point on the unit circle at angle -5π/2 .

(0,-1)

The coordinate point on the unit circle at angle -2π .

(1,0)

A measurement of an angle where a full rotation is expressed as 360 of it.

Degree

The exact value of tan π/2, tan 3π/2, csc 0, csc π, csc 2π, sec π/2, sec 3π/2, cot 0, cot π, and cot 2π.

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The multiplier for converting degrees to radians.

πradians/180°

The exact value of csc π/4, csc 3π/4, sec π/4, and sec 7π/4.

√2

The exact value of sin π/4, sin 3π/4, cos π/4, and cos 7π/4.

√2/2

The exact value of tan π/3, tan 4π/3, cot π/6, and cot 7π/6.

√3

The exact value of sin π/3, sin 2π/3, cos π/6, and cos 11π/6.

√3/2

The exact value of tan π/6, tan 7π/6, cot π/3, and cot 4π/3.

√3/3

The coordinate point on the unit circle at angle 3π.

(-1,0)

The coordinate point on the unit circle at angle 4π/3.

(-1/2, -√3/2)

The coordinate point on the unit circle at angle 2π/3.

(-1/2, √3/2)

The coordinate point on the unit circle at angle -60º .

(1/2, -√3/2)

The coordinate point on the unit circle at angle π/3.

(1/2, √3/2)

The coordinate point on the unit circle at angle 315º.

(√2/2, -√2/2)

The coordinate point on the unit circle at angle π/4.

(√2/2, √2/2)

The coordinate point on the unit circle at angle 11π/6 .

(√3/2, -1/2)

The coordinate point on the unit circle at angle π/6.

(√3/2, 1/2)

The exact value of sin 3π/2, cos π, tan 3π/4, tan 7π/4, csc 3π/2, sec π, cot 3π/4, and cot 7π/4.

-1

The exact value of sin 7π/6, sin 11π/6, cos 2π/3, and cos 4π/3.

-1/2

The exact value of csc 7π/6, csc 11π/6, sec 2π/3, and sec 4π/3.

-2

The exact value of csc 4π/3, csc 5π/3, sec 5π/6, and sec 7π/6.

-2√3/3

The exact value of csc 5π/4, csc 7π/4, sec 3π/4, and sec 5π/4.

-√2

The exact value of sin 5π/4, sin 7π/4, cos 3π/4, and cos 5π/4.

-√2/2

The exact value of tan 2π/3, tan 5π/3, cot 5π/6, and cot 11π/6.

-√3

The exact value of sin 4π/3, sin 5π/3, cos 5π/6, and cos 7π/6.

-√3/2

The exact value of tan 5π/6, tan 11π/6, cot 2π/3, and cot 5π/3.

-√3/3

The exact value of sin 0, sin π, sin 2π, cos π/2, cos 3π/2, tan 0, tan π, tan 2π, cot π/2, and cot 3π/2.

0

The exact value of sin π/2, cos 0, cos 2π, tan π/r, tan 5π/4, csc π/2, sec 0, sec 2π, cot π/4, and cot 5π/4.

1

The exact value of sin π/6, sin 5π/6, cos π/3, and cos 5π/3.

1/2

The multiplier for converting radians to degrees.

180°/πradians

The exact value of csc π/6, csc 5π/6, sec π/3, and sec 5π/3.

2

The number of radians to add or subtract in order to find a coterminal angle.

2π

The exact value of csc π/3, csc 2π/3, sec π/6, and sec 11π/6.

2√3/3

The number of degrees to add or subtract in order to find a coterminal angle.

360°

What is formed by an initial side and a terminal side, both of which are connected to a single vertex point.

Angle

The direction a terminal side of an angle moves for negative angles.

Clockwise

The inverse trigonometric function of sine.

Cosecant

The trigonometric function that is equal to the x-value divided by the radius in the Unit Circle, or the adjacent leg divided by the hypotenuse in a right triangle.

Cosine

The inverse trigonometric function of tangent.

Cotangent

Angles that share the same initial side and terminal side.

Coterminal Angles

The direction a terminal side of an angle moves for positive angles.

Counterclockwise

The trigonometric function that is equal to the y-value divided by the x-value in the Unit Circle, or the opposite leg divided by the adjacent leg in a right triangle.

Tangent

The section of the coordinate plane where all trig functions are positive.

Quadrant I

The section of the coordinate plane where only sin and csc are positive.

Quadrant II

The section of the coordinate plane where only tan and cot are positive.

Quadrant III

The section of the coordinate plane where only cos and sec are positive.

Quadrant IV

A measurement of an angle where the radius and arc length are equal. A full rotation is about 6.28 of these.

Radian

In a unit circle, its length is always 1. It is also the equivalent of the hypotenuse of the special right triangles formed within the unit circle.

Radius

The inverse trigonometric function of cosine.

Secant

The trigonometric function that is equal to the y-value divided by the radius in the Unit Circle, or the opposite leg divided by the hypotenuse in a right triangle.

Sine

When an angle has its vertex at the origin and its initial side on the positive x-axis.

Standard Position