Question

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

Answer 1

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

Answer 2

we have that
angle t=
`(10 \pi )/(3)`

we know that

`(10 \pi )/(3)=((9 \pi )/(3)+ ( \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= ( \pi)/(3) \\ x=-1*cos ( \pi )/(3) \\ x=- (1)/(2)`

Find the y-coordinate in the unit circle

`y=r*sin t`

`r=1 \\ t= ( \pi)/(3) \\ y=-1*sin ( \pi )/(3) \\ y=- ( √(3))/(2)`

the terminal point is
`(- (1)/(2),- ( √(3))/(2) )`

therefore

the answer is

`(- (1)/(2),- ( √(3))/(2) )`