3. Unit Circle

In Exercises 25–30, use an identity to find the value of each expression. Do not use a calculator.sec² 23° - tan² 23°

In Exercises 31–38, find a cofunction with the same value as the given expression.sin 7°

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3.tan α = cot(α + 10°)

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

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3.sin(2θ + 10°) = cos(3θ - 20°)

In Exercises 31–38, find a cofunction with the same value as the given expression.tan 𝜋9

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3.cot(5θ + 2°) = tan(2θ + 4°)

In Exercises 31–38, find a cofunction with the same value as the given expression.cos 2𝜋5

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3.sec(3β + 10°) = csc(β + 8°)

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

In Exercises 41–43, find the exact value of each of the remaining trigonometric functions of θ.cos θ = 2/5, sin θ < 0

Determine whether each statement is true or false. See Example 4.tan 28° ≤ tan 40°

Determine whether each statement is true or false. See Example 4.cos 28° < sin 28°(Hint: sin 28° = cos 62°)

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.csc 20° < csc 30°