NBT Mathematics: Trigonometry Flashcards

What is the range of y = sin x?

Answer: [−1, 1]

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

Simplify: cos²θ − sin²θ

Answer: cos(2θ)

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

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

Answer: 5/13

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

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

Answer: 45° to the left

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

Which of the following is NOT a correct reduction formula?

Answer: sin(180° + θ) = sin θ

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

The value of sin(−60°) is:

Answer: −√3/2

Sine is an odd function: sin(−60°) = −sin 60° = −√3/2.

In a right-angled triangle, the angle of elevation from a point 20 m from the base of a tower to its top is 45°. The height of the tower is:

Answer: 20 m

tan 45° = height/20 → height = 20 × 1 = 20 m.