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Find the terminal point P(x, y) on the unit circle determined by the given value of t. t = – 5pi P(x, y) =

User Artur Keyan
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1 Answer

15 votes
15 votes

A unit circle is parametrized by the functions sine and cosine, that is, in a unit cricle


P(x,y)=(\cos t,\sin t)

In our case we want to know the value of the point if t=-5pi. Then


P(x,y)=(\cos (-5\pi),\sin (-5\pi))

Now, since the sine function is odd and the cosine function is even we have:


\begin{gathered} P(x,y)=(\cos (-5\pi),\sin (-5\pi)) \\ =(\cos 5\pi,-\sin 5\pi) \\ =(-1,0) \end{gathered}

Therefore the terminal point is (-1,0).

User Heypiotr
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