Referring to the diagram below find the exact value of sin t

Referring to the diagram below, find the exact value of sin theta. Referring to the diagram in problem #8, find the exact length of arc s opposite the angle theta.

Solution

given point is (-3,-sqrt(3) )

the given points is (rcos,rsin)

now comparing rcos = -3 , rsin = -3sqrt(3)

rcos/rsin = -3/-3sqrt(3)

cot = 1/sqrt(3)

= +/3

= 4/3

arc length is radius

so squaring and adding points

r^2 (cos^2 + sin^2 )= (-3)^2 + (3sqrt3)^2

r^2 (1) = 9 +27

r^2 =36

r=6

arc length is 6