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= - 𝜋/6

P(x, y) =

Answer 1

Solution: Any point P(x, y) on a circle of radius ‘r’ and centered at origin is represented by (rcosθ, rsinθ) where θ is a parameter.

In this question, t is the parameter.

Here, t = - π/6 and r = 1

P(x, y) = [(1)cos(-π/6), (1) sin (-π/6)]

P(x, y) = [cos(π/6), -sin(π/6)]

P(x, y) = [√3/2, -1/2]

Answer 2

t= - 𝜋/6

Angle in the 4th quadrant, so

x is positive and y is negative

x = cos (–𝜋/6) = √3/2

y = sin (–𝜋/6) = –1/2

P(x, y) = (√3/2, –1/2)