Question

Given f(x)=1+sinX and get g(x)=cos 2X
Calculate the points of intersection of the graph f and g for x€{180°;360°}

Answer 1

f(x)=g(x)
1+sinx=cos2x=1-sin^2 x
change variable sinx = u
1+u=1-u^2
u^2+u=0
u=0 or u=-1
or x=0deg, 180 deg or x=270 (or -90deg).

Answer 2

cos(2X) = 1 - 2 sin^2(X)

1 + sin(X) = 1 - 2 sin^2(X)

solve for sin(X) , match solutions for x€{180°;360°}