Answer:
[tex](\frac{-\sqrt{2}}{2},\frac{\sqrt{2}}{2})[/tex]
Step-by-step explanation:
Unit circle has a radius of 1.
So x=cos(3pi/4)=-sqrt(2)/2 and y=sin(3pi/4)=sqrt(2)/2
So the ordered pair is (-sqrt(2)/2 , sqrt(2)/2)
The terminal point for the unit circle that is determine by the [tex]$\frac{3 \pi}{4} $[/tex] radians is
[tex]$\left( -\frac{1}{\sqrt 2}, \frac{1}{\sqrt 2} \right) . $[/tex]
We know the coordinates of the terminal point will be :
[tex]$x= \cos \left( \frac{3 \pi}{4} \right)$[/tex] and [tex]$y= \sin \left( \frac{3 \pi}{4} \right)$[/tex]
Therefore,
[tex]$x= \cos \left( \pi - \frac{ \pi}{4} \right)$[/tex]
[tex]$x= - \cos \frac{\pi}{4}$[/tex]
[tex]$=-\frac{1}{\sqrt 2}$[/tex]
And
[tex]$y= \sin \left( \frac{3 \pi}{4} \right)$[/tex]
[tex]$y = \sin \left( \frac{\pi}{2} + \frac{\pi}{4} \right)$[/tex]
[tex]$=\cos \frac{\pi}{4}$[/tex]
[tex]$=\frac{1}{\sqrt 2}$[/tex]
Therefore the terminal points are : (x, y) = [tex]$\left( -\frac{1}{\sqrt 2}, \frac{1}{\sqrt 2} \right) . $[/tex]
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