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1.7 Trigonometry

1.7 Trigonometry

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Question 158
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

1.7 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.7 Trigonometry

317 exam-style questions on OCR (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.

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