Skip to content

Course home

Sign up

Trigonometric Identities and Equations

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190
Question 79

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

A sketch of the curves y = 2cos²θ and y = 2 − sinθ on axes spanning 0° to 360° and y = 0 to 3.

a.

Show that the equation 2−sin⁡θ=2cos⁡2θ2 - \sin\theta = 2\cos^2\theta2−sinθ=2cos2θ can be expressed in the form 2sin⁡2x−sin⁡x=02\sin^2 x - \sin x = 02sin2x−sinx=0

[2]
b.

Solve the inequality 2−sin⁡θ>2cos⁡2θ2 - \sin\theta > 2\cos^2\theta2−sinθ>2cos2θ 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.

Question bank