Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Find the values of other five trigonometric functions cosx = -1\2,x lies in third quadrant

Q (1) Find the values of other five trigonometric functions

\small \cos x = -\frac{1}{2}  , x lies in third quadrant.

Answers (1)

Solution 
\cos x = -\frac {1}{2}
   \because \sec x = \frac{1}{\cos x} = \frac{1}{-\frac {1}{2}} = -2
x lies in III quadrants.  Therefore sec x is negative

\sin ^{2}x +\cos^{2}x = 1 \\ \sin^{2}x = 1 - \cos^{2}x\\ \sin^{2}x = 1 -\left ( -\frac{1}{2} \right )^{2}\\ \sin^{2}x = 1 - \frac{1}{4} = \frac{3}{4}\\ \sin x = \sqrt{\frac{3}{4}} = \pm \frac{\sqrt{3}}{2}
    x lies in III quadrants.  Therefore sin x is negative
\therefore \sin x= - \frac{\sqrt{3}}{2}

\because cosec \ x = \frac {1}{\sin x}= \frac{1}{- \frac{\sqrt{3}}{2}} =- \frac{2}{\sqrt{3}}

x lies in III quadrants.  Therefore cosec x is negative

\tan x = \frac{\sin x}{\cos x} = \frac {-\frac{\sqrt{3}}{2}}{-\frac{1}{2}} = \sqrt{3}
x lies in III quadrants.  Therefore tan x is positive

\cot x = \frac{1}{\tan x} = \frac{1}{\sqrt{3}}
x lies in III quadrants.  Therefore cot x is positive
 

Posted by

Safeer PP

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Single Girl Child Scholarship 2024: Registration extended till January 10; eligibility criteria, amount
anam-khan

CBSE wants international boards reined in; letter to education ministry seeks directions for AIU
anam-khan

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14

Latest Question