The coordinates of the point on the unit circle at an angle -225°° are [tex](\frac{-\sqrt{2} }{2} , \frac{\sqrt{2}} {2} )[/tex].
What are coordinates of the point?
" The coordinates of the point is defined as the pair of such points which represents the exact location of the point."
What is unit circle?
" Unit circle means a circle with radius equals to 1unit."
Formula used
Equation of the circle with center (0, 0) and radius r
[tex]x^{2} +y^{2} =r^{2}[/tex]
Coordinates of the point on the circle (rcosθ , rsinθ)
cos(-θ) = cosθ
sin (-θ) = -sinθ
cos ([tex]\frac{3\pi }{2}[/tex] -θ) = -cosθ
sin ([tex]\frac{3\pi }{2}[/tex] -θ) = -sinθ
According to the question,
Given θ = -225°
Unit circle 'r' = 1
Therefore Coordinates are,
'x' coordinates represented by rcosθ
'y' coordinates represented by rsinθ
Substitute the value of r and θ in the coordinates of the point we get,
x = rcosθ
= 1 × cos (-225°)
= cos (225°)
= cos ( 270° - 45°)
[tex]=cos(\frac{3\pi }{2} -\frac{\pi }{4} )[/tex]
[tex]= - sin(\frac{\pi }{4}) \\= - \frac{1}{\sqrt{2} } \\=-\frac{\sqrt{2} }{2}[/tex]
y = rsinθ
= 1 × sin (-225°)
= -sin (225°)
= -sin ( 270° - 45°)
[tex]=-sin(\frac{3\pi }{2} -\frac{\pi }{4} )[/tex]
[tex]= -( - cos(\frac{\pi }{4})) \\= \frac{1}{\sqrt{2} } \\=\frac{\sqrt{2} }{2}[/tex]
Hence, coordinates of the point on the unit circle at an angle -225°° are [tex](\frac{-\sqrt{2} }{2} , \frac{\sqrt{2}} {2} )[/tex].
Learn more about coordinates of the point here
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