Trigonometry Flashcards

Which of the following is equal to sin(π - x)?

Answer: sin(x)

By the identity sin(π - x) = sin(x), the answer is sin(x).

If cos(θ) = 3/5 and θ is in the fourth quadrant, what is sin(θ)?

Answer: -4/5

Using sin²θ + cos²θ = 1 gives |sin θ| = 4/5, and since θ is in Q4, sin θ = -4/5.

What is the period of the function f(x) = tan(3x)?

Answer: π/3

The period of tan(kx) is π/k, so for k = 3 the period is π/3.

Simplify: (1 - cos²x) / sin(x), for sin(x) ≠ 0.

Answer: sin(x)

Since 1 - cos²x = sin²x, dividing by sin(x) gives sin(x).

What is the exact value of cos(150°)?

Answer: -√3/2

cos(150°) = cos(180° - 30°) = -cos(30°) = -√3/2.

If sin(α) = 1/3, what is sin(2α)?

Answer: 4√2/9

sin(2α) = 2sin(α)cos(α); cos(α) = √(1 - 1/9) = 2√2/3, so sin(2α) = 2·(1/3)·(2√2/3) = 4√2/9.

What is the range of f(x) = 3sin(x) + 1?

Answer: [-2, 4]

Since sin(x) ∈ [-1, 1], multiplying by 3 gives [-3, 3], then adding 1 gives [-2, 4].