3. Unit Circle

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

Find the exact values of s in the given interval that satisfy the given condition.

[0, 2π) ; sin s = -√3 / 2

In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of 0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋. 6 3 2 3 6 6 3 2 3 6 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.

In Exercises 11–18, continue to refer to the figure at the bottom of the previous page. csc 4𝜋/3

Each figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the six circular function values of θ.

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2. sin 45°

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. csc(β + 40°) = sec(β - 20°)

Find a calculator approximation to four decimal places for each circular function value. cos (-0.2443)

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

ω = 0.91 radian per min, t = 8.1 min

Express each angular speed in radians per second. 6 revolutions per second

Find the exact value of s in the given interval that has the given circular function value.

[π/2, π] ; sin s = 1/2

Find each exact function value. See Example 2. sin 7π/6

Find the exact value of s in the given interval that has the given circular function value.

[π, 3π/2] ; tan s = √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 a calculator approximation to four decimal places for each circular function value. See Example 3. tan 4.0203

Find exact values of the six trigonometric functions for each angle A.