Find the terminal point p(x, y) on the unit circle determined by the given value of t.
t = -7π/6, p(x, y) = (-3/√2, -1/2).

Solution:

We have any point (x, y) on the unit circle of radius ‘r’ centered at origin which is (rcosθ, rsinθ)/(rcost, rsint).

Here, t = -7π/6 and r = 1

∴ Required point (x, y) = (rcost, rsint)

= [(1)cos (-7π/6), (1)sin(-7π/6)]

= [cos 7π/6, -sin7π/6] [∵ cos(-θ) = cosθ and sin (-θ) = -sinθ]

Using allied angles,

cos(7π/6) = cos [π + (π/6)] = - cos(π/6) = -√3/2

-sin(7π/6) = -sin [π+ (π/6)] = -[-sin(π/6)] = 1/2

Therefore, the required point is (-√3/2, 1/2)

Find the terminal point p(x, y) on the unit circle determined by the given value of t.
t = -7π/6, p(x, y) = (-3/√2, -1/2).

Summary:

The terminal point p(x, y) on the unit circle determined by the given value of t, t = -7π/6, p(x, y) = (-3/√2, -1/2) is (-√3/2, 1/2).