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Trigonometric Identities and Equations

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Question 3

The diagram shows parts of the curves y=10cos⁡2θy = 10\cos^2\thetay=10cos2θ and y=9−3tan⁡θcos⁡θy = 9 - 3\tan\theta \cos\thetay=9−3tanθcosθ, where θ \theta\,θ is in degrees.

Two curves are shown on axes labelled θ and y, with open circles on the curve labelled y = 9 − 3tanθ cosθ at 90° and 270°.

a.

Show that the equation 9−3tan⁡θcos⁡θ=10cos⁡2θ9 - 3\tan\theta \cos\theta = 10\cos^2\theta9−3tanθcosθ=10cos2θ can be expressed in the form 10sin⁡2x−3sin⁡x−1=010\sin^2 x - 3\sin x - 1 = 010sin2x−3sinx−1=0

[2]
b.

Solve the inequality 9−3tan⁡θcos⁡θ>10cos⁡2θ9 - 3\tan\theta \cos\theta > 10\cos^2\theta9−3tanθcosθ>10cos2θ for 0∘≤θ<360∘0^\circ \leq \theta < 360^\circ0∘≤θ<360∘

[5]
Markscheme

Trigonometric Identities and Equations Questions

  1. A Level
  2. /Maths
  3. /Trigonometric Identities and Equations

322 exam-style questions on Edexcel A Level Maths Trigonometric Identities and Equations, covering 10.1 Angles in all four Quadrants, 10.2 Exact Values of Trigonometric Ratios, 10.3 Trigonometric Identities, 10.4 Solving Trigonometric Equations, 10.5 Harder Trigonometric Equations, and 10.6 Equations and Identities. Each one has a worked solution and a mark scheme showing where the marks go.

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