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.

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)

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eudora eudora · Answer 2 · 2019-10-06T03:23:55+02:00

Answer:

Terminal point will be (-[tex]\frac{1}{2}[/tex], -[tex]\frac{\sqrt{3} }{2}[/tex])

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 = [tex]\frac{4\pi }{3}[/tex]

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

x coordinate = r cost

= [tex]1\times cos\frac{4\pi }{3}[/tex]

= [tex]cos(\frac{3\pi }{2}-\frac{\pi }{3})[/tex]

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

= -[tex]\frac{1}{2}[/tex]

y- coordinate = r sint

= [tex]1\times sin\frac{4\pi }{3}[/tex]

= -[tex]sin(\frac{2\pi }{3}-\frac{\pi }{3})[/tex]

= -[tex](1\times sin\frac{\pi }{3})[/tex]

= -[tex]\frac{\sqrt{3} }{2}[/tex]

Therefore, terminal point will be (-[tex]\frac{1}{2}[/tex], -[tex]\frac{\sqrt{3} }{2}[/tex])