3. Unit Circle

In Exercises 17–20, θ is an acute angle and sin θ and cos θ are given. Use identities to find tan θ, csc θ, sec θ, and cot θ. Where necessary, rationalize denominators.__sin θ = 6, cos θ = √137 7

In Exercises 21–24, θ is an acute angle and sin θ is given. Use the Pythagorean identity sin²θ + cos²θ = 1 to find cos θ.sin θ = 6/7

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

In Exercises 21–24, θ is an acute angle and sin θ is given. Use the Pythagorean identity sin²θ + cos²θ = 1 to find cos θ.__sin θ = √398

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2.tan 25.4°

In Exercises 28–29, find a cofunction with the same value as the given expression.sin 70°

In Exercises 25–30, use an identity to find the value of each expression. Do not use a calculator.sin² 𝜋 + cos² 𝜋 10 10

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2.cos(θ + 20°)

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°)