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

Question

Find the terminal point P(x, y)

 on the unit circle determined by the given value of t.

t = −5𝜋

P(x, y) =

Answer 1

I assume we always want to start at the point (0, 1), which is at 3 o'clock on the circle, and walk along the circumference (clockwise, because a negative number such as -5π goes clockwise) for a distance of -5π radians.

One complete walk around the circle is a distance of 2π radians, so we're going for 2 and a half complete walks (clockwise) around the circle from our starting point at 3 o'clock.

That will leave us off at the point at 9 o'clock, whose coördinates are (-1, 0).

Answer 2

(x, y) = (cos(-5π) , sin(-5π)) = (-1, 0)

Answer 3

-5π = -4π - π

-5π is coterminal with -π

Can you answer now?