3. Unit Circle

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°

Concept Check Work each problem. Without using a calculator, determine which of the following numbers is closest to sin 115°: -0.9, -0.1, 0, 0.1, or 0.9.

Find the exact value of s in the given interval that has the given circular function value.

[ π , 3π/2] ; sec s = ―2√3/3

On the unit circle, in which quadrant are both $\cos$ and $\cot$ negative?

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. b = 8, c = 11

Determine whether each statement is true or false. See Example 4. cot 30° < tan 40°

Determine whether each statement is true or false. See Example 4. tan 28° ≤ tan 40°

What is the value of $\tan \frac{\pi }{3}$ on the unit circle?

Find the approximate value of s, to four decimal places, in the interval [0 , π/2] that makes each statement true.

sec s = 1.0806

Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. 300°

Which of the following explains why $\cos (60°)$ equals $\sin (30°)$ using the unit circle?

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 approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.

cos s = 0.9250