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How do you find the endpoint of the radius of the unit circle that corresponds 9π/2 radians?

Answer 1

Charles Autterson

First, convert #(9pi)/2# to less than #2pi#

#(9pi)/2-(8pi)/2=pi/2#

So, #(9pi)/2# is coterminal to #pi/2#

Now, #pi/2# is also #90^o# making the endpoint (0,1)

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Answer 2

Kai Anderson

To find the endpoint of the radius of the unit circle that corresponds to ( \frac{9\pi}{2} ) radians, we use the trigonometric functions sine and cosine.

The coordinates of any point on the unit circle can be represented as ( (\cos(\theta), \sin(\theta)) ), where ( \theta ) is the angle measured in radians.

For ( \theta = \frac{9\pi}{2} ):

( \cos\left(\frac{9\pi}{2}\right) = 0 ) (since cosine is 0 at ( \frac{\pi}{2} ) and ( \frac{5\pi}{2} ), and it repeats every ( \pi ) radians)
( \sin\left(\frac{9\pi}{2}\right) = 1 ) (since sine is 1 at ( \frac{\pi}{2} ) and ( \frac{5\pi}{2} ), and it repeats every ( \pi ) radians)

So, the endpoint of the radius corresponding to ( \frac{9\pi}{2} ) radians on the unit circle is ( (0, 1) ).

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Answer from HIX Tutor

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