1.5 Trigonometry

Sketch and use graphs of the sine, cosine and tangent functions, for angles of any size and using either degrees or radians.

Includes, for example, y = 3 sin x, y = 1 − cos 2x and y = tan(x + ¼π).

Taught in: Sine, cosine and tangent of any angle, The graphs of sin, cos and tan, Stretching and shifting trig graphs · 19 questions

Use the exact values of the sine, cosine and tangent of 30°, 45° and 60°, and of related angles.

Examples: cos 150° = −½√3; sin ¾π = 1/√2.

Taught in: Exact values of sin, cos and tan · 7 questions

Use the notations sin⁻¹x, cos⁻¹x and tan⁻¹x to denote the principal values of the inverse trigonometric relations.

No specialised knowledge of these functions is required, but they should be understood as examples of inverse functions.

Taught in: sin⁻¹, cos⁻¹, tan⁻¹ and principal values · 6 questions

Use the identities sin θ / cos θ ≡ tan θ and sin²θ + cos²θ ≡ 1.

For example, in proving identities, simplifying expressions and solving equations.

Taught in: Trig equations that need an identity first, Proving trig identities, The two identities: tan θ ≡ sin θ ÷ cos θ and sin²θ + cos²θ ≡ 1 · 14 questions

Find all the solutions of simple trigonometrical equations that lie in a specified interval (general forms of solution are not included).

Examples: solve 3 sin 2x + 1 = 0 for −π < x < π; solve 3 sin²θ − 5 cos θ − 1 = 0 for 0° ≤ θ ≤ 360°.

Taught in: Trig equations that need an identity first, Equations like sin 2x = k and cos(x − 30°) = k, Solving sin x = k, cos x = k and tan x = k · 18 questions