Edexcel A-Level Mathematics AS P2.6.2 Solving Trigonometric Equations Questions

Practise Edexcel IAL Mathematics P2.6.2 by simplifying equations with identities, reducing them to algebraic forms, solving for every valid angle and reporting the required precision.

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: 9]

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

(a)

Solve, for $0 \leq \theta < 180^\circ$ , the equation
$7\sin 2\theta = 5\cos 2\theta$
giving your answers, in degrees, to one decimal place.

[ 4 ]

$7\sin 2\theta=5\cos 2\theta$ $\tan 2\theta=\frac57$ $2\theta=\arctan\left(\frac57\right)$ $\theta=17.8^\circ,\ 107.8^\circ\text{ (awrt)}$

(b)

Solve, for $0 \leq x < 2\pi$ , the equation
$24\tan x = 5\cos x$
giving your answers, in radians, to 3 decimal places.

[ 5 ]

$24\tan x=5\cos x$ $24\sin x=5\cos^2 x$ $24\sin x=5(1-\sin^2x)$ $5\sin^2x+24\sin x-5=0$ $\sin x=\frac15$ $x=0.201,\ 2.940\text{ (awrt)}$

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Edexcel A-Level Mathematics AS P2.6.2 Solving Trigonometric Equations Questions question 1

Question (a)

Question (b)