How do you find the terminal point p(x, y) on the unit circle determined by the giving value of t = -3π/4

Solution:

A unit circle is one that has a radius of 1 unit. The problem can be represented by the figure below:

The point P(x, y) can be determined as follows:

Since △OQP is a right-angled triangle we can use the trigonometric ratios accordingly.

sin(-3π/4) = QP/OP

-1/√2 = QP/1

QP = -1/√2

Therefore y = -1/√2

Also,

cos(-3π/4) = OQ/OP

-1/√2 = OQ/1

OQ = 1/√2

Therefore x = 1/√2

Hence the point Point P(x, y) has the coordinates (1/√2, -1/√2 ).

How do you find the terminal point p(x, y) on the unit circle determined by the giving value of t = -3π/4

Summary:

The terminal point p(x, y) on the unit circle determined by the giving value of t = -3π/4 is determined to be P (1/√2, -1/√2 ).