3. Unit Circle

Find each exact function value. See Example 2.

tan 3π/4

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

r = 12 m , ω = 2π/3 radians per sec

Find each exact function value. See Example 2.

csc 11π/6

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

v = 9 m per sec , r = 5 m

Find each exact function value. See Example 2. cos (―4π/3)

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)