AS LEVEL MATHS TRIGONOMETRIC IDENTITIES, Exercises of Mathematics

AS LEVEL MATHS TRIGONOMETRIC IDENTITIES

Typology: Exercises

2025/2026

Uploaded on 06/04/2026

jk008
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TRIGONOMETRIC IDENTITIES & EQUATIONS
More definitions: The tan function, Pythagorean Identity, Co-function
tan and Pythagorean Identity
Co-function Identity
Solving Equations
sin 𝜃
cos 𝜃
tan 𝜃
Equations with Linear Inputs
Change the range
Solve for new range first
Solve these for 𝑥, 𝜃, etc.
Pure Year 1, Chapter 10
Solve sin 𝑥 = 0.6, giving your answers to the nearest degree.
Solve cos 𝜃 = −0.3, 180° < 𝜃 < 180°,
giving your answers to 1dp.
Solve for < 𝑥 < 90°, giving your answers to 1dp.
5sin 2𝑥 20 ° + 2cos(2𝑥 20 = 0
pf2

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TRIGONOMETRIC IDENTITIES & EQUATIONS

More definitions: The tan function, Pythagorean Identity, Co-function

tan and Pythagorean Identity Co-function Identity Solving Equations sin 𝜃 cos 𝜃 tan 𝜃 Equations with Linear Inputs

  • Change the range
  • Solve for new range first
  • Solve these for 𝑥, 𝜃, etc.

Pure Year 1, Chapter 10

Solve sin 𝑥 = 0. 6 , giving your answers to the nearest degree. Solve cos 𝜃 = − 0. 3 , − 180 ° < 𝜃 < 180°, giving your answers to 1dp. Solve for 0 ° < 𝑥 < 90 °, giving your answers to 1 dp. 5 sin 2 𝑥 − 20 ° + 2 cos( 2 𝑥 − 20 )° = 0

Identities and Equations – more challenging

a) Show that 10 sin^2 𝜃 − 7 sin 90 − 𝜃 + 2 3 + 2 cos 𝜃 ≡ 4 − 5 cos 𝜃 b) Hence, solve for − 180 ° ≤ 𝑥 ≤ 180° 10 sin^2 2𝑥 − 7 sin 90 − 2𝑥 + 2 3 + 2 cos 2𝑥 = 6 cos^2 2𝑥