Sec 3 A-Math Trigonometric Functions & Graphs topical questions

Express 72° in radians, giving your answer in terms of π.

Write down the exact values of sin 30° and cos 60°.

Solve the equation cos x = 1/2 for 0° ≤ x ≤ 360°.

State the amplitude and the period of the curve y = 4 sin(3x).

State the amplitude, period, maximum value and minimum value of y = 2 cos(x/2) − 1.

Given that sin θ = 2/3 and θ is acute, find the exact values of cos θ and tan θ.

Solve the equation 2 cos x = −1.2371 for 0° ≤ x ≤ 360°, giving your answers correct to 1 decimal place.

Solve the equation 2 sin²x − sin x − 1 = 0 for 0° ≤ x ≤ 360°.

Prove the identity (1 − cos²A)(1 + cot²A) = 1.

Solve the equation tan x = 2.4 for 0° ≤ x ≤ 360°, giving your answers correct to 1 decimal place.

The curve y = a sin(bx) + 1, where a is a positive constant and b is a positive integer, has a maximum value of 5 and a period of 90°. Find the values of a and b.

Solve the equation sin 2x = 0.5 for 0° ≤ x ≤ 360°.

The graph of y = a cos(bx) + c has maximum points at (0°, 6) and (180°, 6), and a minimum point at (90°, −2). Find the values of a, b and c.

Prove the identity tan θ sin θ + cos θ = sec θ.

Given that 5 sin²θ + 3 cos²θ = 4 and that θ is acute, find the exact value of sin θ.