Question

Find the acute angle theta such that 2cos theta = 3sin theta

Answer 1

Answer:

2cosx = 3sinx

2cosx - 3sinx=0

Divide both parts by sqrt(2^2+3^2) = sqrt(13).

(2/sqrt(13))*cosx-(3/sqrt(13))*sinx=0

Let arccos(2/sqrt(13)) = alpha

Then cos(alpha) = 2/sqrt(13), sin(alpha)=3/sqrt(13)

cos(alpha)*cosx - sin(alpha)*sinx = 0

cos(alpha-x) = 0

cos(x-alpha) = 0

x-alpha = pi/2+pi*n

x=alpha + pi/2+pi*n

x= arccos(2/sqrt(13)) + pi/2+pi*n, where n is any integer.