If 3sinx = 2cosx determine the value of x.

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3sinx = 2cosx

let us square both sides:

==> 9sin^2 x = 4cos^2 x..........(1)

We kow that :

sin^2 x + cos^2 x = 1

==> sin^2 x = 1 - cos^2 x

==> Substitute in (1):

==> 9(1-cos^2 x) = 4cos^2 x

==: 9 - 9cos^2 x = 4cos^2 x

Combine like terms:

==> 9- 13cos^2 x = 0

==> 13cos^2 x = 9

==: cos^2 x = 9/13

==> cosx = +-3/sqrt13

==> x= arccos(3/sqrt13) + 2npi

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