NBT NBT Mathematics: Trigonometry 4

Question 1

What is tan(360° − θ) equivalent to?

Accepted Answer

−tan θ

Answer

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

Question 2

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

Accepted Answer

135°

Answer

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

Question 3

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

Accepted Answer

cos θ

Answer

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

Question 4

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

Accepted Answer

39

Answer

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

Question 5

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

Accepted Answer

y = sec x

Answer

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

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