Edexcel IAL Mathematics P2.6.2 solving trigonometric equations

The direct evidence stresses interval discipline: reduce the equation to sin, cos or tan, solve the algebraic form and list all angles in the required range.

Exam points

Convert equations such as 4tanθ + 5sinθ = 0 into clear sin or cos factors.
Solve quadratic forms in sin x or tan 2θ before finding all valid angles.
Give answers in the requested interval, with exact radians or rounded degrees as specified.

[Maximum number: 5]

In this question you must show detailed reasoning.

Solutions relying entirely on calculator technology are not acceptable.

Hence solve for $-\frac{\pi}{2} \leqslant x \leqslant \frac{\pi}{2}$

(3 \cos 2 x-\tan 2 x) \cos 2 x=2

Solving the quadratic from part (a) gives
$\sin 2x=\frac{-1\pm\sqrt{13}}{6}$
or approximately 0.434 and -0.768.
Then solve $2x=\sin^{-1}(0.434)$ or $2x=\sin^{-1}(-0.768)$ in the range $-\frac{\pi}{2}\le x\le\frac{\pi}{2}$ .
x=-1.13, -0.438, 0.225, 1.35.
M1 A1 M1 A1 A1

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P2.6.2 - Solving trigonometric equations question 1