Question

Find sin2a if sina=3/5 and a is in quadrant 2

Answer 1

sin(a)= $\frac{3}{5}$

To find sin(2a) = 2*sin(a)*cos(a), we ned to find cos(a)

We know that,

sin²(a) + cos²(a) = 1

cos(a) = $\sqrt{( 1- sin^2 a)}$

cos(a) = $\sqrt{1- ( \frac{3}{5} )^2} = \sqrt{1- \frac{9}{25}} = \sqrt{ \frac{16}{25}} = \frac{4}{5}$

Thus, cos(a) = +- $\frac{4}{5}$

We know a is in second quadrant and thus cos(a) is -$\frac{4}{5}$ because cosine is always negative in the second quadrant.

Therefore,

sin(2a) = 2*sin(a)*cos(a) = $2* \frac{3}{5} * \frac{-4}{5} = \frac{-24}{25}$