Verified Answer :

taskmasters

Note: On the unit circle, P (x, y) = (cos(t), sint(t))
Terminal point of t = 10pi/3 is ( -1/2, -sqrt(3)/2)

calculista

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



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