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Katen [24]
3 years ago
14

Find the terminal point determined by t= 10pi/3.

Mathematics
2 answers:
Pie3 years ago
6 0
We have that
angle t=\frac{10 \pi }{3}

we know that
\frac{10 \pi }{3}=(\frac{9 \pi }{3}+ \frac{ \pi }{3} )

the terminal point belong to the III quadrant
so
the x-coordinate is negative
the y-coordinate is negative

Find the x-coordinate  in the unit circle
x=r*cos t
r=1 \\ t= \frac{ \pi}{3} \\ x=-1*cos \frac{ \pi }{3} \\ x=- \frac{1}{2}

Find the y-coordinate  in the unit circle
y=r*sin t
r=1 \\ t= \frac{ \pi}{3} \\ y=-1*sin \frac{ \pi }{3} \\ y=- \frac{ \sqrt{3}}{2}

the terminal point is (- \frac{1}{2},- \frac{ \sqrt{3}}{2} )

therefore

the answer is
(- \frac{1}{2},- \frac{ \sqrt{3}}{2} )



Nastasia [14]3 years ago
5 0
Note: On the unit circle, P (x, y) = (cos(t), sint(t))
Terminal point of t = 10pi/3 is <span>( -1/2, -sqrt(3)/2)</span>
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See attachment for graph

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