Question

if tan x=1/2 and x is the third quadrant find sin x and cos x
plz reply​

Answer 1

answer is in the attachment hope this helps

Answer 2

Answer:

$sin x =-\sqrt{\frac{1}{5} }$

$cos x=-\frac{2}{\sqrt{5} }$

given:

tan x=1/2

 x is the third quadrant

To find :

find sin x and cos x

Explanation :

tan x = 1/2

x lies in third quadrant

sin and cos values "-ve" in third quadrant

$tan^2x+1=sec^2x$

$(\frac{1}{2})^2+1=sec^2x$

$\frac{1}{4}+1=sec^2x\\ sec^2x=\frac{5}{4}$

We know that

$secx=\frac{1}{cosx}$

$cos^2x=\frac{4}{5}$

$cos x = \sqrt{\frac{4}{5} }$

$cos x = + or - \frac{2}{\sqrt{5} }$

$cos x=-\frac{2}{\sqrt{5} }$

As we know that

$sin^2 x = 1-cos^2 x$

$sin^x=1-\frac{4}{5}$

$sin^2x=\frac{5-4}{5}$

$sin^2x=\frac{1}{5}$

$sin x=+ or -\sqrt{\frac{1}{5} }$

$sin x =-\sqrt{\frac{1}{5} }$

To know more about trignometric functions refer:

https://brainly.com/question/29253466

https://brainly.com/question/29286780

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