Question

What are the coordinates of the terminal point determined by t=10pi/3

Answer 1

we know that

10*pi/3------> convert to degrees------> 10*180/3=600 degrees

600=360+240

240 degrees belong to the III quadrant

so

the x-coordinate is negative

the y-coordinate is negative

240°=180°+60°

60 degrees is the angle to find the terminal point

let

∅=60°

in the unit circle

r=1 units

x=-r*cos ∅----> x=-cos 60------> x=-(1/2)

y=-r*sin ∅----> y=-sin 60------> y=-(√3)/2

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

therefore

the answer is the option D

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