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

Question

Find the terminal point  on the unit circle determined by the given value of :

t= x/2

t= -pi/2

t= pi/3

t= -pi/3

Answer 1

Given the angle (in radians), we want to find the location this occurs on the unit circle. As a reminder, the unit circle begins at an angle of 0 on the far right, going counter-clockwise straight up we reach π/2, continuing counter-clockwise to the far left we reach π, continuing counter-clockwise straight down we reach 3π/2, continuing counter-clockwise we return to the far right at 2π or 0. The circle is defined as having a radius of 1.

At π/2, the circle touches the point (0,1)

At -π/2 (or 3π/2) the circle touches the point (0,-1)

At π/3, the circle touches the point (1/2, √3/2)

At -π/3 (or 5π/3), the circle touches the point (1/2, -√3/2)