Skip to content

Course home

Sign up

1.8 E: Trigonometry

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169
Question 112

A student is asked to solve the equation sin⁡2x=1\sin^2 x = 1sin2x=1 for 0°⩽x⩽360°0° \leqslant x \leqslant 360°0°⩽x⩽360°.

The student writes:

Step 1: sin⁡x=1\sin x = 1sinx=1

Step 2: x=90°x = 90°x=90°

a.

Explain the error the student has made in Step 1.

[1]
b.

State the correct solutions of sin⁡2x=1\sin^2 x = 1sin2x=1 for 0°⩽x⩽360°0° \leqslant x \leqslant 360°0°⩽x⩽360°.

[2]
c.

A second student solves the equation sin⁡xcos⁡x=sin⁡x\sin x\cos x = \sin xsinxcosx=sinx for 0°⩽x<360° 0° \leqslant x < 360°\,0°⩽x<360° by dividing both sides by sin⁡x\sin xsinx, obtaining cos⁡x=1\cos x = 1cosx=1 and hence x=0°x = 0°x=0°. Explain what is wrong with this method, and give the complete solution set.

[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