Question

If cosx = -3/5 and π < x < 3π/2, find the values of sin 2x

Answer 1

Given: cosx = \(\frac{-3}{5}\)

To find: sin2x

We know that, sin2x = 2 sinx cosx …(i) 

Here, we don’t have the value of sin x. 

So, firstly we have to find the value of sinx 

We know that,

cos²x + sin²x = 1

Putting the values, we get

It is given that π < x < \(\frac{3\pi}{2}\)

\(\Rightarrow\) sinx = \(\frac{-4}{5}\)

Putting the value of sinx and cosx in eq. (i), we get

sin2x = 2sinx cosx