3. Unit Circle

Use the formula v = r ω to find the value of the missing variable.

v = 12 m per sec, ω = 3π/2 radians per sec

Find each exact function value. See Example 2.

cos 7π/4

The formula ω = θ/t can be rewritten as θ = ωt. Substituting ωt for θ converts s = rθ to s = rωt. Use the formula s = rωt to find the value of the missing variable.

r = 6 cm, ω = π/3 radians per sec, t = 9 sec

Find each exact function value. See Example 2.

sin (4π/3)

The formula ω = θ/t can be rewritten as θ = ωt. Substituting ωt for θ converts s = rθ to s = rωt. Use the formula s = rωt to find the value of the missing variable.

s = 6π cm, r = 2 cm, ω = π/4 radian per sec

Find each exact function value. See Example 2.

sec 23π/6

The formula ω = θ/t can be rewritten as θ = ωt. Substituting ωt for θ converts s = rθ to s = rωt. Use the formula s = rωt to find the value of the missing variable.

s = 3π/4 km, r = 2 km, t = 4 sec

Find each exact function value. See Example 2.

tan 5π/6

Find a calculator approximation to four decimal places for each circular function value. See Example 3. sin 0.6109

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

Find each exact function value.

tan π/3

Find the angular speed ω for each of the following.

a gear revolving 300 times per min

Find the angular speed ω for each of the following.

a wind turbine with blades turning at a rate of 15 revolutions per minute

Find a calculator approximation to four decimal places for each circular function value. See Example 3. tan 4.0203

Find each exact function value.

sin ( ―5π/6)