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Mathematics Standard Level for the IB Diploma Self-assessment answers: 9 Trigonometric equations and identities 1 π 5π 2kπ for k ∈ . 1. 3x = arcsin or 6 2 6 3x x π 5π 13π 17π , , , , ... 6 6 6 6 π 5π 13π 17π , , , 18 18 18 18 [4 marks] 2 2 2. Using the identity sin x = 1 – cos x: 2 2 2sin x – cos x = 1 2cos x + cos x – 1 = 0 (2cos x – 1)(cos x + 1) = 0 cos x = x= 1 or –1 2 π , π 3 3. sin x (sin x − [8 marks] 3 cos x) = 0 sin x = 0 or tan x = 3 x = 0, 60, 240, 360 [6 marks] 2 4. Using double angle formula, cos 2θ = 1 – 2 sin θ 2 2 sin θ + sin θ – 1 = 0 (2 sin θ + 1)(sin θ – 1) = 0 sin θ = 1 or 1 2 θ = 90, 210 or 330 Copyright Cambridge University Press 2013. All rights reserved. [6 marks] Page 1 of 1