3. Unit Circle

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

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

Find the linear speed v for each of the following.

the tip of a propeller 3 m long, rotating 500 times per min (Hint: r = 1.5 m)

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

θ = 3π/4 radians, t = 8 sec

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

ω = 2π/3 radians per sec, t = 3 sec

In Exercises 31–38, find a cofunction with the same value as the given expression. csc 25°

Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)

cos 2

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

cot 6.0301

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

A thread is being pulled off a spool at the rate of 59.4 cm per sec. Find the radius of the spool if it makes 152 revolutions per min.

Find the linear speed v for each of the following.

a point on the equator moving due to Earth's rotation, if the radius is 3960 mi