Can someone explain?!?!?!!?

Question

The following is the work for using the unit circle in find the exact value of sin 17π/3

a)which step has the first error?

b)explain the error

1)find the coterminal angle

17π/3-2π=5π/3

2) using the unit circle, the point at 5π/3 is (1/2,-sqart3/2)

3)because sin is the y value, sin17π/3=-sqart/2

Answer 1

sin17pi/3 = sin(17pi/3 - 18pi/3) = sin-pi/3 = sin-60

add or subtract from 17pi/3 any integer multiple of 2p such as 18pi/3 = 6pi= 3(2pi)

=-sin60

= -(sqr3)/2

Youre 1st step 17pi/3 -2pi is on the right track

17pi/3 - 6pi/3 = 11pi/3

subtract another 2pi = 6pi/3 leaving 11pi/3 -6pi/3 = 5pi/3

1st step you have got that far

sin(17pi/3) = sin(5pi/3)

Your 2nd step looks good too

the point on a unit circle with angle 5pi/3 is

(1/2, -(sqr3)/2

3rd step is correct too, except you just mistakenly

typed t instead of 3

-(sqr(t))/2 instead of -(sqr3)/2

Answer 2

1) First mistake:

17π/3 - 2π = 17π/3 - 6π/3 = 11π/3 Needs common denominator

11π/3 = 2(11π/6)

sin(2(11π/6)) = 2sin(11π/6)cos(11π/6) By the double angle formula

Using the unit circle for 11π/6 -> (√3/2, -1/2)

sin(17π/3) = 2(-1/2)(√3/2)

= -√3/2

Answer 3