Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • If sin⁡θ=-4/5 and θ lies in third quadrant then the value of cos⁡〖θ/2〗 is

If \sin \theta = - \frac{4}{5}  and θ lies in third quadrant then the value of \cos \frac{ \theta }{2} is

A.\frac{1}{5}

B.\frac{-1}{\sqrt{10}}

C.\frac{-1}{\sqrt{5}}

D.\frac{1}{\sqrt{10}}

Answers (1)

The answer is the option (c)

   \\ \sin \theta = - \frac{4}{5}, \theta \text{lies in third quadrant} \\\\

\\ \cos \theta = - \sqrt {1 - \left( - \frac{4}{5} \right) ^{2}}= - \frac{3}{5} \\\\ \cos \theta =2\cos ^{2}\frac{ \theta }{2} - 1 \\\\ - \frac{3}{5}=2\cos ^{2}\frac{ \theta }{2} - 1 \\\\ \cos ^{2}\frac{ \theta }{2}=\frac{1}{5} \\\\ \cos \frac{ \theta }{2}= - \frac{1}{\sqrt {5}}~ \\\\

\left[ As,~\frac{ \pi }{2}<\frac{ \theta }{2}<\frac{3 \pi }{4} \right]

Hence, correct option is (c).  

Posted by

infoexpert21

View full answer

Similar Questions

Latest Question