NBT NBT Mathematics: Trigonometry 5

Question 1

What is the range of y = sin x?

Accepted Answer

[−1, 1]

Answer

The sine function oscillates between −1 and 1 inclusive, so its range is [−1, 1].

Question 2

Simplify: cos²θ − sin²θ

Accepted Answer

cos(2θ)

Answer

The double angle identity states cos(2θ) = cos²θ − sin²θ.

Question 3

If tan θ = 5/12 and θ is acute, find sin θ.

Accepted Answer

5/13

Answer

With opposite = 5 and adjacent = 12, hypotenuse = 13; sin θ = 5/13.

Question 4

The horizontal shift (phase shift) in y = sin(x + 45°) is:

Accepted Answer

45° to the left

Answer

Adding 45° inside the function shifts the graph 45° to the left.

Question 5

Which of the following is NOT a correct reduction formula?

Accepted Answer

sin(180° + θ) = sin θ

Answer

sin(180° + θ) = −sin θ (Quadrant III, sine is negative), not +sin θ.

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