3. Unit Circle

Use a calculator to evaluate each expression. cos 75°29' cos 14°31' - sin 75°29' sin 14°31'

Find a calculator approximation to four decimal places for each circular function value. See Example 3. cos (-1.1519)

The unit circle has been divided into twelve equal arcs, corresponding to t-values of

0, 𝜋/6, 𝜋/3, 𝜋/2, 2𝜋/3, 5𝜋/6, 𝜋, 7𝜋/6, 4𝜋/3, 3𝜋/2, 5𝜋/3, 11𝜋/6, and 2𝜋

Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.

<IMAGE>

cos 5𝜋/6

Find each exact function value.

csc ( ―11π/6)

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.

csc 60°

Give the exact value of each expression. See Example 5. tan 30°

Find a calculator approximation to four decimal places for each circular function value. See Example 3.

sec 2.8440

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. sec(3β + 10°) = csc(β + 8°)

For each value of s, use a calculator to find sin s and cos s, and then use the results to decide in which quadrant an angle of s radians lies.

s = 51

Which of the following expressions is equivalent to $\sin (22°)$?

Find a calculator approximation to four decimal places for each circular function value. See Example 3. csc (―9.4946)

Find each exact function value. See Example 2.

cos 7π/4