NBT Mathematics: Trigonometry Flashcards

What is tan(360° − θ) equivalent to?

Answer: −tan θ

Using the reduction formula tan(360° − θ) = −tan θ (Quadrant IV, tangent is negative).

If tan θ = −1 and θ ∈ (90°, 180°), find θ.

Answer: 135°

The reference angle for tan = 1 is 45°; in Quadrant II, θ = 180° − 45° = 135°.

Which of the following equals sin(90° + θ)?

Answer: cos θ

Using the reduction formula, sin(90° + θ) = cos θ.

The Cosine Rule states: a² = b² + c² − 2bc cos A. If b = 5, c = 7, A = 60°, find a².

Answer: 39

a² = 25 + 49 − 2(5)(7)(0.5) = 74 − 35 = 39.

Which function has a range of (−∞, −1] ∪ [1, ∞)?

Answer: y = sec x

The secant function sec x = 1/cos x has range y ≤ −1 or y ≥ 1, i.e., (−∞, −1] ∪ [1, ∞).

Prove: (sin θ + cos θ)² = 1 + 2sin θ cos θ. The missing step uses:

Answer: sin²θ + cos²θ = 1

Expanding gives sin²θ + 2sin θ cos θ + cos²θ; replacing sin²θ + cos²θ with 1 gives 1 + 2sin θ cos θ.

The area of triangle ABC with sides a = 8, b = 6, and included angle C = 30° is:

Answer: 12

Area = ½ab sin C = ½ × 8 × 6 × sin 30° = 24 × 0.5 = 12.