How many and which values of satisfy in the interval ?

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

How many and which values of xx satisfy sin⁡3x=sin⁡x\sin 3x = \sin x in the interval 0≤x<2π0 \le x < 2\pi? (a) {0,  π4,  3π4,  π2,  5π4,  7π4}\{0,\;\dfrac{\pi}{4},\;\dfrac{3\pi}{4},\;\dfrac{\pi}{2},\;\dfrac{5\pi}{4},\;\dfrac{7\pi}{4}\} (b) {0,  π4,  3π4,  π,  5π4,  7π4}\{0,\;\dfrac{\pi}{4},\;\dfrac{3\pi}{4},\;\pi,\;\dfrac{5\pi}{4},\;\dfrac{7\pi}{4}\} (c) {π4,  3π4,  5π4,  7π4}\{\dfrac{\pi}{4},\;\dfrac{3\pi}{4},\;\dfrac{5\pi}{4},\;\dfrac{7\pi}{4}\} (d) {0,  π4,  3π4,  5π4,  7π4,  2π}\{0,\;\dfrac{\pi}{4},\;\dfrac{3\pi}{4},\;\dfrac{5\pi}{4},\;\dfrac{7\pi}{4},\;2\pi\}

Related theory

Browse the problem library