Skip to content

Course home

Sign up

1.8 E: Trigonometry

EasyMediumHard
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374
Question 47
a.

Show that

cos⁡2xsin⁡x+sin⁡2xcos⁡x≡csc⁡x,x≠nπ2,  n∈Z \frac{\cos 2x}{\sin x} + \frac{\sin 2x}{\cos x} \equiv \csc x, \quad x \neq \frac{n\pi}{2}, \; n \in \mathbb{Z} sinxcos2x​+cosxsin2x​≡cscx,x=2nπ​,n∈Z
[3]
b.

In a study of fluid dynamics, the pressure coefficient PPP is modeled by the equation

(cos⁡2θsin⁡θ+sin⁡2θcos⁡θ)2=7−cot⁡θ \left( \frac{\cos 2\theta}{\sin \theta} + \frac{\sin 2\theta}{\cos \theta} \right)^2 = 7 - \cot \theta (sinθcos2θ​+cosθsin2θ​)2=7−cotθ

Hence solve this equation for 0<θ<π0 < \theta < \pi0<θ<π, giving your answers to 3 significant figures as appropriate.

[5]
c.

Using the result from part (a), or otherwise, find the exact value of

∫π6π4(cos⁡2xsin⁡x+sin⁡2xcos⁡x)cot⁡x dx \int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \left( \frac{\cos 2x}{\sin x} + \frac{\sin 2x}{\cos x} \right) \cot x \, dx ∫6π​4π​​(sinxcos2x​+cosxsin2x​)cotxdx
[3]
Markscheme

1.8 E: Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.8 E: Trigonometry

317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank