Find the terminal point P(x, y) on the unit circle determined by the given value of t. t = -π/6

Solution: 

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

Also θ can be replaced by ‘t’ when 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]

Example:

Find the terminal point P(x, y) on the circle of radius 2 units determined by the given value of t. t = 3π/4

Solution:

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

Also θ can be replaced by ‘t’ when t is the parameter.

Here, t = -3π/4 and r = 2

P(x, y) = [(2)cos(3π/4), (2)sin (3π/4)]

P(x, y) = [2(-1/√2), 2(1/√2)]

P(x, y) =(-√2, √2)

Find the terminal point P(x, y) on the unit circle determined by the given value of t. t = -π/6

Summary:

The terminal point P(x, y) on the unit circle determined by the given value of t, t = -π/6 is [√3/2, -1/2].