logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
0 votes

If $\cos x=-\large\frac{\sqrt{15}}{4}$ and $\large\frac{\pi}{2}$$ \lt x $$ \lt \pi$ ,find the value of $\sin x$

$\begin{array}{1 1}(A)\;\large\frac{1}{2}&(B)\;\large\frac{1}{4}\\(C)\;\large\frac{1}{3}&(D)\;\large\frac{1}{5}\end{array} $

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • $\sin ^2x+\cos ^2x=1$
  • $\sin x=\sqrt{1-\cos^2x}$
Clearly $x$ lies in the II quadrant in which $\sin x$ and $cosec x$ are positive and all the other trigonometric functions are negative.
Now,$\cos x=-\large\frac{\sqrt{15}}{4}$
$\sin x=\sqrt{1-\cos ^2x}$
$\Rightarrow \sqrt{1-(-\large\frac{\sqrt 5}{4})^2}$
$\Rightarrow \sqrt{1-\large\frac{1 5}{16}}$
$\Rightarrow \sqrt{\large\frac{16-15}{16}}$
$\Rightarrow \large\frac{1}{4}$
$\therefore \sin x=\large\frac{1}{4}$
Hence (B) is the correct answer.
answered Apr 22, 2014 by sreemathi.v
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...