The value of ∅ is 60° or [tex]\frac{\pi }{3}[/tex] radians.
What is a unit circle?
'The Unit Circle is a circle with a radius of 1'
According to the given problem,
Let (x , y) = [tex](\frac{1}{2} , \frac{\sqrt{3} }{2} )[/tex]
If rectangular coordinates (x , y) = (r , ∅) which are the polar coordinates,
x = rcos∅ ; y = rsin∅
We know, r = 1, for a unit circle,
Therefore,
x = cos∅ and y = sin∅
Now, putting value of x in x=cos∅, we are getting,
cos∅ = [tex]\frac{1}{2}[/tex]
⇒ ∅ = [tex]cos^{-1}[/tex]([tex]\frac{1}{2}[/tex])
⇒ ∅ = 60° or [tex]\frac{\pi }{3}[/tex] radians
Hence, we can conclude that the possible value of ∅ is [tex]\frac{\pi }{3}[/tex] radians.
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