CAIE IGCSE Additional Math 10.5 solve trigonometric equations

Use this trig-equations page to factor or transform equations, find all solutions in the interval and state exact radian answers when required.

Exam points

Transform trig equations into solvable forms using identities or factorisation.
Find all degree or radian solutions within the interval specified in the question.
Give exact answers in terms of π when the equation is set in a radian interval.

[Maximum number: 5]

It is given that $y=3\tan^2x$ for $0^\circ<x<360^\circ$ .

Find all values of x such that $\frac{dy}{dx}=3\sec x\operatorname{cosec}x$ .

$\begin{aligned}6\tan x\sec^2x-3\sec x\operatorname{cosec}x&=0\\3\sec x(2\tan x\sec x-\operatorname{cosec}x)&=0\end{aligned}$
B1
$2\tan^2x=1$ oe
B1
$\tan x=\pm\sqrt{\frac12}$
M1
$x=35.3^\circ,\ 144.7^\circ,\ 215.3^\circ,\ 324.7^\circ$
A2; A1 for any two correct answers, no extras.

All question bank results loaded

10.5. Solve trigonometric equations question 1