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Trigonometric Identities and Equations

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Question 18

The diagram shows parts of the curves y=6cos⁡2θy = 6\cos^2\thetay=6cos2θ and y=5−sin⁡θy = 5 - \sin\thetay=5−sinθ, where θ \theta\,θ is in degrees.

Diagram of the curves y = 6cos²θ and y = 5 − sinθ on axes labelled θ and y for 0° ≤ θ < 360°.

a.

Show that the equation 6sin⁡2θ−sin⁡θ−1=06\sin^2\theta - \sin\theta - 1 = 06sin2θ−sinθ−1=0 can be expressed in the form 5−sin⁡θ=6cos⁡2θ5 - \sin\theta = 6\cos^2\theta5−sinθ=6cos2θ

[2]
b.

Solve the inequality 5−sin⁡θ>6cos⁡2θ5 - \sin\theta > 6\cos^2\theta5−sinθ>6cos2θ 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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