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Trigonometry

If sin theta is equals to minus 4 by 5 and theta lies in third quadrant then cos theta by 2 equals to

Shravan yadav

8 Years agoGrade

2 Answers

Pavan Karri

8 Years ago

theta belongs to Q₃, theta/2 belongs to Q₂. Therefore cos( theta/2) is -ve. sin theta= -4/5 that implies cos theta= -3/5.

use multiple ratios formula and cos (theta/2)=-2/(5)^1/2.

Hope you are satisfied.

Soumendu Majumdar

8 Years ago

Dear Student,

since $\theta$ is in 3^rd quadrant so both $sin\theta$ and $cos\theta$ are negative.

Now using Pythagorean triplet we know $3^2 + 4^2 = 5^2$

so since $sin\Theta =-4/5$

so $cos\Theta =-3/5$

Now using the formula,

$1+cos\Theta =2cos^2(\Theta /2)$

$\Rightarrow cos^2(\Theta /2)= 1/5$

$\Rightarrow cos(\Theta /2)=$ + $1/\sqrt{5}$

Now since $\Theta$ is in 3^rd quadrant so $\Theta /2$ must be in 2^nd quadrant and so $cos(\Theta /2)$ must be negative.

Hence

$cos(\Theta /2)=-1/\sqrt{5}$

Hope it helps!

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