Question

If $\tan \theta =\frac{3}{4}$ Find $3\cos A+4\sin A$

Answer 1

Given $tan\theta =\frac{3}{4}$

Using trignomatric identities if $tan\theta =\frac{3}{2}$

then $AC=\sqrt{9+16}=5$

and

$sin\theta =sinaA=\frac{3}{5}$ & $cos\theta =cosA=\frac{4}{5}$

then $3cosA+4sonA=3\times \frac{4}{5}+4\times \frac{3}{5}$

$3cosA+4sinA=\frac{24}{5}$