CAIE A-Level Mathematics AS 1.5.5 Trig Equations Questions

Practise reducing trigonometric equations with identities or substitutions, solving for the trig ratio and generating every valid angle in the specified interval.

Exam points

Rewrite a trigonometric equation using identities or substitutions to obtain an equation in one trigonometric ratio, then solve the resulting algebraic equation.
Find every angle in the specified interval that satisfies the equation, using the sign and periodicity of the trigonometric ratio to include all valid solutions.
Check the interval and endpoint conditions to determine whether an equation has zero, one or several solutions.

[Maximum number: 3]

Hence solve the equation $\cos 2 x(7 \tan 2 x-5 \cos 2 x)=1$ for $0^{\circ}<x<180^{\circ}$ .

Figure for Question CAIE A-Level Mathematics AS 1.5.5 Trig Equations Questions question 1 — CAIE A-Level Mathematics AS

Attempt solution of their 3 term equation and correct process to find at least 1
value of $\sin x$ or $\sin 2 x$ or $\sin \theta$
Expect (5 s-3)(s+2)=0, s=3 / 5.

x=18.4
Or greater accuracy.
B1 SC if no solution to the quadratic.

x=71.6 or ( 90 - their 18.4) or greater accuracy;
and no other solutions for
$0^{\circ}<x<180^{\circ}$

A1FT

WWW
B1 SC FT if no solution to the quadratic.
B1 SC both correct in radians, 0.322, 1.25.

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CAIE A-Level Mathematics AS 1.5.5 Trig Equations Questions question 1