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(2, 8)y = f(x)RO146xy
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15616817481.5%
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Integration — areasDue Fri
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7 dot points · 3 topicsEdit
Trigonometric functions
MA-T2.1 · MA-T3.1 · MA-T3.2
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23403:02
Solve 2sin²x = 1 + cos x for 0 ≤ x ≤ 2π, giving your answers in exact form. 3 marks
2cos²x + cos x − 1 = 0
(2cos x − 1)(cos x + 1) = 0
x = π/3, π, 5π/3
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Question 2 of 504:18
Solve 2sin²x = 1 + cos x for 0 ≤ x ≤ 2π.
Worked solution
Using sin²x = 1 − cos²x the equation becomes 2cos²x + cos x − 1 = 0.

Factorising, (2cos x − 1)(cos x + 1) = 0, so cos x = ½ or cos x = −1.

In the domain, x = π/3, 5π/3 and x = π.
Marking criteria3 marks
1 markUses a Pythagorean identity to obtain a quadratic in cos x
1 markSolves the quadratic for both values of cos x
1 markStates all three solutions in the domain in exact form
Mark lostMA-T3.2
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