3. Unit Circle

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

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°

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 the linear speed v for each of the following.

the tip of the minute hand of a clock, if the hand is 7 cm long

Use the formula ω = θ/t to find the value of the missing variable.

θ = 2π/9 radian , ω = 5π/27 radian per min

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

Find the linear speed v for each of the following.

a point on the edge of a flywheel of radius 2 m, rotating 42 times per min

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

Find each exact function value.

csc ( ―11π/6)

Find a formula for the area of each figure in terms of s.

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