If \( A \sin \theta=3 \) and \( A \cos \theta=4 \) then ' \( \theta \) ' will be-

Question

If \( A \sin \theta=3 \) and \( A \cos \theta=4 \) then ' \( \theta \) ' will be-

Answer 1

Given that

\(Asinθ = 3\)

⇒  \(sinθ = 3/A\) ... (1)

Also, 

\(Acosθ = 4\)

⇒ \(cosθ = 4/A\) ... (2)

Squaring (1) and (2), and adding them both we get

\(sin^2θ + cos^2θ = \frac{9}{A^2} + \frac{16}{A^2} = \frac{25}{A^2}\)

⇒ \(1 = \frac{25}{A^2}\)

⇒ \(A = 5\) 

Putting Value of \(A\) in (1), we get

\(sinθ = \frac{3}{5} \)

⇒ \(θ = 37°\)