Question

How many solutions are there to the equation 3cosx=sinx on the interval [0, 2π]1236

Answer 1

3 cos x = sin x

Divide each side by cos x

3 cos x / cos x = sin x / cos x

3 = tan x

Take the inverse tan of each side

tan ^-1(3) = tan^-1( tan (x))

Since tan has a period of pi, there are 2 solutions in the interval of [0, 2pi]