Trigonometric Equations Questions with Solutions

14 questions4 easy7 medium3 hard

A trigonometric equation is an equation involving trigonometric functions of an unknown angle, such as 2 sin x = 1. This topic covers finding principal solutions (usually between 0 and 2 pi) and general solutions, which include all possible angles. The key general solutions are: sin x = sin a gives x = n pi + (-1)^n a, cos x = cos a gives x = 2n pi +/- a, and tan x = tan a gives x = n pi + a, where n is any integer. Exam questions involve reducing an equation to one of these standard forms, often by factorising or using identities, and then counting the number of solutions in a given interval. Always check that solutions do not make any term in the original equation undefined. Practise the trigonometric equations questions below, each with a step-by-step solution.

All Questions Easy Medium Hard

Q1.
Consider the graphs of the functions $f (x) = 2 cos (\frac{x}{2}) + 3$ and $g (x) = 4$ . The number of points of intersection of the two graphs in the interval $[0, 4 π]$ is:
A. 4B. 3C. 1D. 2
easyAsked in NIMCET 2026View solution ›
Q2.
The general solution of $3 cos x + s in x = 3$ is
A. $2 nπ \pm \frac{π}{6}$ B. $2 nπ \pm \frac{π}{3}$ C. No solutionD. $nπ \pm \frac{π}{6}$
easyAsked in NIMCET 2011View solution ›
Q3.
The solutions of the equation $4 cos^{2} x + 6 s in^{2} x = 5$ are
A. $x = nπ \pm \frac{π}{4}$ B. $x = nπ \pm \frac{π}{3}$ C. $x = nπ \pm \frac{π}{2}$ D. $x = nπ \pm \frac{2 π}{3}$
easyAsked in NIMCET 2022View solution ›
Q4.
What is the general solution of the equation $t an θ + co tθ = 2$ ?
A. $θ = nπ + \frac{π}{4}$ B. $θ = \frac{nπ}{2} + \frac{π}{8}$ C. $θ = \frac{nπ}{2} + \frac{π}{6}$ D. $θ = \frac{nπ}{2} + \frac{π}{4}$
easyAsked in NIMCET 2025View solution ›