Unit Circle

reference angle

the acute angle formed by the terminal side of an angle in standard position and the x-axis

Find the coordinates of the point (x, y) shown on the unit circle. x = _____ y = _____

-1/2, -sqrt3/2

Select all angle measures for which cos theta = 1/2

-60° 660°

cos(270°) = _____ sin(270°) = _____ tan(270°) = _____ cos(0°) = _____ sin(0°) = _____ tan(0°) = _____

0 -1 undefined 1 0 0

to find the trigonometric functions for any angle:

1. identify the reference angle, merp 2. find the value of the function at the reference angle, merp 3. determine the sign of the value based on the quadrant containing the terminal side

Find the value of the function for θ. sin(45°) = ?

sqrt2/2

The _____ models the periodic nature of trigonometric functions.

unit circle

For the given angle 0, identify the reference angle, merp, θ = 11pi/6 merp = ?

pi/6

Which of the following statements shows how to calculate the reference angle for θ = 11pi/6

2pi - θ

Use the steps to determine the exact value of sin(−135)°. Identify the reference angle, θ.

45°

For which angle θ is cos θ = −1?

540°

Select all angle measures for which sin theta= -sqrt2/2

5pi/4 7pi/4 13pi/4

Identify the reference angle ø for each given angle, theta. When theta= 300 degrees, ø= When theta= 225 degrees, ø= When theta= 480 degrees, ø= When theta= -210 degrees, ø=

60, 45, 60, 30

The angles that share the same sine value as sin(45°) have terminal sides in quadrant _____

II

Determine the sign of the value based on the quadrant containing the terminal side. Because −135° terminates in quadrant _____ the sine value is negative.

III

The angles that share the same tangent value as tan(45°) have terminal sides in quadrant

III

The angles that share the same cosine value as cos 45° have terminal sides in quadrant _____

IV

quadrantal angle

an angle in standard position that terminates on the x- or y-axis

unit circle

circle with radius 1, centered at origin

Select all that have a value of 0.

cos pi/2 sin 0 tan pi

if the terminal side of an angle in standard positions intersects the unit circle at (x, y), then:

cos θ = x sin θ = y tan θ = y/x

The unit circle can be used to find the value of a trigonometric function at any angle, with the _____ acting as reference angles for all others.

first quadrant angle

what are the coordinates of the point where the terminal side of an angle measuring pi/3 radians intersects the unit circle?

pi/3 = 60° (x, y) = (cos pi/3, sin pi/3) (x, y) = (1/2, sqrt3/2)