NBT Mathematics: Trigonometry Flashcards

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

Answer: 4/5

Using the Pythagorean identity, cos θ = √(1 − sin²θ) = √(1 − 9/25) = √(16/25) = 4/5.

What is the exact value of sin 30° × cos 60°?

Answer: 1/4

sin 30° = 1/2 and cos 60° = 1/2, so their product is 1/4.

In which quadrant is θ if sin θ 0?

Answer: Quadrant IV

In Quadrant IV, sine is negative and cosine is positive, matching the given conditions.

Simplify: sin²x + cos²x + tan²x − sec²x

Answer: 0

sin²x + cos²x = 1, and tan²x − sec²x = −1, so the full expression equals 1 + (−1) = 0.

The period of y = sin(2x) is:

Answer: π

The period of y = sin(bx) is 2π/b; with b = 2, the period is 2π/2 = π.

Solve for θ ∈ [0°, 360°]: 2sin θ − 1 = 0

Answer: θ = 30° or 150°

2sin θ = 1 gives sin θ = 1/2; the solutions in [0°, 360°] are θ = 30° and θ = 150°.

In triangle ABC, angle B = 90°, AB = 5 and BC = 12. What is sin A?

Answer: 12/13

AC = √(5² + 12²) = 13 (hypotenuse); sin A = opposite/hypotenuse = BC/AC = 12/13.