SOLUTION: find the exact coordinates of the point on a circle of radius 5 at an angle of 5pi/3

Algebra ->  Trigonometry-basics -> SOLUTION: find the exact coordinates of the point on a circle of radius 5 at an angle of 5pi/3      Log On


   

Question 1153711: find the exact coordinates of the point on a circle of radius 5 at an angle of 5pi/3
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

find the exact coordinates of the point on a circle of radius 5 at an angle of 5pi/3
an angle of 5pi%2F3 (300 degrees) is in the positive x direction
if the circle is centered at the origin and the 5pi%2F3 is measured counter clockwise from the x-axis, then the point on the circle would be in Quadrant IV, and the distance from the origin to the x- coordinate of the point on the circle would be 5%2Acosine%285pi%2F3+%29+ and the+y-coordinate would be 5%2Asine+%285pi%2F3%29
x=5%2Acosine%285pi%2F3+%29=5%281%2F2%29++=5%2F2
y=5%2Asine+%285pi%2F3%29=+5%28-sqrt%283%29%2F2%29=-5sqrt%283%29%2F2
the exact coordinates:

(5%2F2,-5sqrt%283%29%2F2)