Sec 4 A-Math Further Trigonometry topical questions

Using the compound-angle formulae, show that sin 75° = (√6 + √2)/4.

Given that sin A = 3/5 and A is acute, find the exact values of sin 2A and cos 2A.

Express cos 2A − 3 sin²A in terms of cos A only.

Express 3 cos θ + 4 sin θ in the form R cos(θ − α), where R > 0 and 0° < α < 90°. State the maximum and minimum values of 3 cos θ + 4 sin θ.

Solve the equation 3 sin 2x = 2 for 0° ≤ x ≤ 360°, giving your answers correct to 1 decimal place.

Express 5 sin θ − 12 cos θ in the form R sin(θ − α), where R > 0 and 0° < α < 90°, and hence solve 5 sin θ − 12 cos θ = 6.5 for 0° ≤ θ ≤ 360°, giving your answers correct to 1 decimal place.

Prove the identity sin 2A/(1 + cos 2A) = tan A.

Solve the equation sin(x + 45°) = 0.7 for 0° ≤ x ≤ 360°, giving your answers correct to 1 decimal place.

Solve the equation cos 2x + sin x = 0 for 0 ≤ x ≤ 2π, giving your answers in exact form in terms of π.

It is given that tan A = 1/3. (a) Find the exact value of tan 2A. (b) Hence solve the equation tan 2x = 3/4 for 0° ≤ x ≤ 360°, giving your answers correct to 1 decimal place.

The current in an alternating-current circuit is modelled by I = 6 cos t + 8 sin t, where t is measured in degrees and 0° ≤ t ≤ 360°. (a) Express I in the form R cos(t − α), where R > 0 and 0° < α < 90°. (b) Write down the maximum value of I and the first value of t at which it occurs. (c) Solve 6 cos t + 8 sin t = 8, giving your answers correct to 1 decimal place.