Without solving, how do you determine the number of solutions for the equation sintheta=sqrt3/2 in 0<=theta<2pi?

1 Answer
Salvatore I.
Nov 6, 2016

2 solutions
theta=pi/3 and theta=2pi/3

Explanation:

pi/3 is a remarkable angle for the sinus function and sin(pi/3)=root2(3)/2

on the other hand we know that sin(pi-theta)=sin(pi)cos(theta)-cos(pi)sin(theta)=sin(theta). This implies that if there is a solution at theta=pi/3, there must be another solution at theta=2pi/3

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