The coordinates of the points on unit circle at the given angle 240 degrees is[tex](\frac{-1}{2} ,\frac{-\sqrt{3} }{2} )[/tex]
The formula for calculating Radians is:
[tex]radians= (degrees)[/tex]×[tex]\frac{\pi }{180}[/tex]
Formula for calculating coordinates of point (x, y) on circle:
x=rcosθ
y=rsinθ (where r is the radius of circle for unit circle r=1)
According to the question
we have
θ = 240 degrees and, r =1
so, 240 degrees = 240×[tex]\frac{\pi }{180}[/tex]
⇒240 degrees = [tex]\frac{4\pi }{3}[/tex] (in radians)
Therefore, the coordinates of the points on unit circle at angle [tex]\frac{4\pi }{3}[/tex] is calculated as
[tex]x=(1)cos\frac{4\pi }{3}[/tex] (for unit circle r=1)
[tex]x=\frac{-1}{2}[/tex]
And,
[tex]y=(1)sin\frac{4\pi }{3}[/tex] (for unit circle r=1)
[tex]y=\frac{-\sqrt{3} }{2}[/tex]
Hence, the coordinates of the point on unit circle at angle 240 degrees is [tex](\frac{-1}{2} ,\frac{-\sqrt{3} }{2} )[/tex]
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