solve for x if f[x]=g[x]

Question

given f[x]=Sinx and g[x]=Cos2x and x E[-90;270]

Answer 1

Assuming f(x)=sin(x) and g(x)=cos(2x), sin(x)=cos(2x) when f(x)=g(x).

sin(x)=sin(90-2x),

x=90-2x, 3x=90, x=30 is one solution. sin(30)=sin(150) so x=150 is another solution.

sin(x)=sin(180-x), so sin(180-x)=sin(90-2x),

180-x=90-2x, x=-90 is another solution. -90 is the same as 360-90=270, so x=270 is another solution.

We have 4 solutions in the specified range: x=-90, 30, 150, 270.