sin(2x) = cos(3x)

Question

what is the value of x??

Answer 1

Try 306 degrees or 5.340703 radians

Answer 2

cos(3x) = sin(π/2-3x) = sin(2x)

We can equate the arguments

π/2-3x = 2x

5x=π/2

x=π/10 radians = 18°

cos(54°) = sin(36°) --> 0.58778.. = 0.58778...

Actually 2x = π/2-3x + 2πn or 2x = π-(π/2-3x)+2πn

x= (π+4πn)/10 or x = -(π+4πn)/2

If x=-π/2

cos(-3π/2) = sin(-2π/2) --> 0=0