​ If sinA = 3/5 and π/2 < A < π. Find cos A, tan 2A. ​

Question

If sinA = \(\frac{3}{5}\) and \(\frac{\pi}{2}\) < A < π. Find cos A, tan 2A.

Answer 1

Since sin A > 0 and \(\frac{\pi}{2}\) < A < π, then A is in II Quadrant.

Sin A = \(\frac{3}{5}\)

⇒ sin²A = \(\frac{9}{25}\)

∴ cos²A = 1 – \(\frac{9}{25}\) = \(\frac{16}{25}\)

⇒ cos A = \(\frac{-4}{5}\)  (in II Quadrant)

Now,

tanA = \(\frac{sin\,A}{cos\,A}\) 

= \(\frac{3/5}{4/5}\) = \(-\frac{3}{4}\)

And, 

tan 2A = \(\frac{2tan\,A}{1-tan^2\,A}\)

= \(\frac{2(-3/4)}{1-(-3/4)^2}\)

= \(\frac{-6/4}{7/16}\)

= \(-\frac{24}{7}\)