NBT Mathematics: Trigonometry Flashcards

Solve for θ ∈ [0°, 360°]: cos θ = √3/2

Answer: θ = 30° or 330°

cos 30° = √3/2; cosine is positive in Quadrants I and IV, giving θ = 30° and 360° − 30° = 330°.

The maximum value of y = 5sin(x) + 3 is:

Answer: 8

Maximum of 5sin(x) is 5, so maximum of 5sin(x) + 3 is 5 + 3 = 8.

What is sin(180°)?

Answer: 0

sin 180° = 0; the sine function equals zero at 0°, 180°, and 360°.

Express sin²θ in terms of cos(2θ).

Answer: (1 − cos 2θ)/2

From cos 2θ = 1 − 2sin²θ, rearranging gives sin²θ = (1 − cos 2θ)/2.

A bearing of N60°E means an angle of __ measured clockwise from North.

Answer: 60°

N60°E is a compass bearing indicating 60° measured clockwise from North towards East.

If cos 2A = 0 and A ∈ [0°, 90°], then A =

Answer: 45°

cos 2A = 0 → 2A = 90° → A = 45° (within the given range).

The function y = tan x is undefined at x = 90° because:

Answer: cos 90° = 0, making division by zero

tan x = sin x / cos x; at x = 90°, cos 90° = 0, so the function is undefined (division by zero).