Question

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

Answer 1

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).