Question

sin theta=3/4 find theta
plzz solve fast and show all steps to solve it.. its urgent​

Answer 1

Given  

\tan( \alpha ) = \frac{3}{4}  

2 \sin( \alpha ) + 3 \cos( \alpha ) = x

Divide the equation by  

\cos( \alpha )  

2 \tan( \alpha ) + 3 = x \sec( \alpha )  

Square both side

{(2 \tan( \alpha ) + 3)}^{2} = {(x \sec( \alpha ) )}^{2}  

{(2 \times \frac{3}{4} + 3 )}^{2} = {x}^{2} {(1 + { \tan( \alpha ) }^{2} ) )}  

{( \frac{9}{2} )}^{2} = {x}^{2} {(1 + \frac{9}{16} )}  

{x}^{2} = \frac{81}{16} \times \frac{4}{25}  

{x}^{2} = \frac{81×16}{25×4}  

x = \sqrt{ \frac{81×16}{25×4} } = + - \frac{18}{5}