Question

hiee mates⭐⭐

plzzz explain properly

I'LL MARK AS BRAINLIEST ☺️☺️

Answer 1

Hola User ......

Basically as u obtained here result as

Cos@ = 1/root 2 and sin@ = -1/root 2 ...

so here we can consider -pi / 4 ...because we know that ....

sin (-@) = - sin @ so.......sin ( - pi/4 ) = - sin (pi/4) = - 1 / root 2

but we know that in case of the cosine ratio ...

cos ( -@) = Cos @

thus here we can say ..... Cos (-pi/4 ) = Cos (pi/4 ) = 1 / root 2

Answer 2

Hope u like my process
=====================
Given
=-=-=-=
$= > \it \sin( \theta ) = - \frac{1}{ \sqrt{2} } \\ \\ \it = > \cos( \theta ) = \frac{1}{ \sqrt{2} } \\ \\ \bf \: \: \: \: \: \: \: \: \: \underline{...now...} \\ \\ dividing \: \: \sin( \theta ) \: \: by \: \: \cos( \theta ) \\ \\ = > \frac{ \sin( \theta ) }{ \cos( \theta ) } = \blue{ \frac{ - \frac{1}{ \sqrt{2} } }{ \frac{1}{ \sqrt{2} } }} = \blue{ - 1} \\ \\ = > \tan( \theta ) = \blue{ - 1} = \blue{\tan(n\pi - \frac{\pi}{4} ) }\\ \\ = > \boxed{ \bf \: \theta = \underline{ \green{n\pi - \frac{\pi}{4}} }}$

Where n =0,1,2,3,...

Now..
=-=-=-=
Putting, n = 0 ,
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

We get, $\theta =- \frac{\pi} {4}$
__-__-__-__-__-__-__-__-__-__
And putting n = 2
=-=-=-=-=-=-=-=-=-=
We get, $\theta = 2\pi - \frac{\pi} {4}$

=> $\theta = \frac {7\pi} {4}$
___________________________
Hence both are correct.

__________________________
Hope this is ur required answer❤️

Proud to help you❤️