Question 310853: Solve the trig equation sin2x = sqrt(3)sinx
Answer by J2R2R(94)   (Show Source):
You can put this solution on YOUR website! Solve the trig equation sin(2x) = sqrt(3)sin(x)
sin(2x) = 2 sin(x) cos(x)
So we have
2 sin(x) cos(x) = sqrt(3) sin(x)
We can cancel sin(x) from both sides which makes sin(x) = 0 a solution i.e. 0, 180, 360, etc.
2 cos(x) = sqrt(3) or cos(x) = sqrt(3)/2 giving x=30 and 330.
So solutions in degrees in the range 0<=x<360 are
0, 30, 180 and 330
which shows there are four solutions for each 360 degrees range.
N.B. bear in mind that a 360 degree range does not take both end points in its range since one end point is the other end point with 360 added to it.
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