Question

Find the terminal point P(x,y) on the unit circle determined by the given value of t=4pi/3. Please enter your answer as an ordered pair. Do not convert fractions to decimal form.

Answer 1

Answer:

Terminal point will be (-$\frac{1}{2}$, -$\frac{\sqrt{3} }{2}$)

Step-by-step explanation:

Terminal point (x, y) on a circle is defined by P(x, y) = ( r cost, r sin t)

Where t is the angle = $\frac{4\pi }{3}$

and Radius of the circle = 1 unit [unit circle]

x coordinate = r cost

                     = $1\times cos\frac{4\pi }{3}$

                     = $cos(\frac{3\pi }{2}-\frac{\pi }{3})$

                     = -$(1\times cos\frac{\pi }{3})$ [angle lies in third quadrant so the value will be negative]

                     = -$\frac{1}{2}$

y- coordinate = r sint

                      = $1\times sin\frac{4\pi }{3}$

                      = -$sin(\frac{2\pi }{3}-\frac{\pi }{3})$

                      = -$(1\times sin\frac{\pi }{3})$

                      = -$\frac{\sqrt{3} }{2}$

Therefore, terminal point will be (-$\frac{1}{2}$, -$\frac{\sqrt{3} }{2}$)

                       

Answer 2

So in your circle their is a terminal point who is assigned by the value of  P(x,y) and lies or determined by teh value of T=4pi/3. To get the coordinates of this terminal point first is to know what is the angle of the T and the answer is (-1/2, -sqrt(3)/2)