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/3

P(x, y) = (. )

Answer 1

t = 5𝜋/3

Angle in the 4th quadrant, so

x is positive and y is negative

The 1st quadrant reference angle is 𝜋/3:

cos (𝜋/3) = 1/2 and sin (𝜋/3) = √3/2

x = cos (5𝜋/3) = +cos (𝜋/3) = 1/2

y = sin (5𝜋/3) = –sin (𝜋/3) = –√3/2

P(x, y) = (1/2, –√3/2)