3.12 Equivalent Trig Functions (HW Quiz)

The function f is given by f(θ) = (csc θ cot θ sin θ) / (cos θ). Which of the following expressions is equivalent to f(θ)?

• csc θ

• sin θ

• sec θ

• tan θ

• x = π/2 and 3π/2

• x = π/4, 3π/2, 5π/4

• x = π/2, 3π/4, 7π/4

• x = π/2

The function f is given by f(θ) = cos(2θ). Which of the following expressions is equivalent to f(θ)?

• 2cos θ

• 1 - 2sin² θ

• 1 - 2cos² θ

• 2 sin θ cos θ

The function g is defined by g(x) = sin(x + π/3). The solutions to which of the following equations on the interval 0 ≤ x ≤ 2π are the solutions to g(x) = 1 on the interval 0 ≤ x ≤ 2π?

• sin x + √3 cos x = 2

• sin x - √3 cos x = 2

• √3 sin x + cos x = 2

• √3 sin x - cos x = 2

The function f is given by f(θ) = cos(θ + 3π/2). What is the value of f(π/3)?

• √3/2

• 1/2

• -1/2

• -√3/2

Given cos(2x) = 3/5 and π/2 ≤ x ≤ π, what is the exact value of sin(x)?

• 2√5/5

• √5/5

• -√5/5

• -2√5/5