NBT NBT Mathematics: Trigonometry 3

Question 1

Express cos(180° − θ) in terms of cos θ.

Accepted Answer

−cos θ

Answer

Using the co-function reduction formula, cos(180° − θ) = −cos θ.

Question 2

The graph of y = cos x has a maximum value at x equal to:

Accepted Answer

0°

Answer

y = cos x reaches its maximum value of 1 at x = 0° (and x = 360°, etc.).

Question 3

Given sin 40° ≈ 0.643, what is cos 50°?

Accepted Answer

0.643

Answer

Since 40° and 50° are complementary angles, cos 50° = sin 40° ≈ 0.643.

Question 4

Solve cos θ = −1 for θ ∈ [0°, 360°].

Accepted Answer

180°

Answer

cos θ = −1 only at θ = 180° within [0°, 360°].

Question 5

What is the value of 2sin 60° − cos 30°?

Accepted Answer

√3/2

Answer

2sin 60° = 2 × (√3/2) = √3 and cos 30° = √3/2, so √3 − √3/2 = √3/2.

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