3. Unit Circle

Which expression is equivalent to $\sin \frac{7\pi }{6}$?

On the unit circle, what is the radian measure of the arc that subtends a central angle of $90°$?

On the unit circle, what relationship do the ratios $\frac{\sin x}{1}$ and $\frac{\cos y}{1}$ share for any real values of $x$ and $y$?

Find the sine, cosine, and tangent of each angle using the unit circle.

$\(\theta\)=-1.18$ rad, $\(\left\)(\(\frac{5}{13}\),-\(\frac{12}{13}\]\right\))$

Find the sine, cosine, and tangent of each angle using the unit circle.

$\(\theta\)=225\(\degree\),\(\left\)(-\(\frac{\sqrt2}{2}\),-\(\frac{\sqrt2}{2}\]\right\))$

Find exact values of the six trigonometric functions for each angle A.

CONCEPT PREVIEW Match each trigonometric function in Column I with its value in Column II. Choices may be used once, more than once, or not at all.

tan 45°

Find each exact function value. See Example 2. sin 7π/6

Graph each function over a one-period interval.

y = - (1/2) csc (x + π/2)

Find exact values or expressions for sin A, cos A, and tan A. See Example 1.

Find exact values or expressions for sin A, cos A, and tan A. See Example 1.

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Use the Pythagorean theorem to find the unknown side length. Then find exact values of the six trigonometric functions for angle B. Rationalize denominators when applicable. See Example 1.

a = 5, b = 12