Question

Question in attachment

Answer 1

Explanation:

Answer 2

`cos(x)=-(√(3) )/(2)`

`sin(x)=(1)/(2)`

`tan(x)=-(1)/(√(3) )`

`csc(x)=2`

`sec(x)=-(2)/(√(3))`

`cot(x)=-√(3)`

Explanation:

(I'll just use x for ease of writing)

We have the trig equation
`cos(x)=-(√(3) )/(2)`, and we know that its terminal side is in the 2nd quadrant. By using a unit circle, we can determine that the angle is
`(5\pi)/(6)` which has an ordered pair of
`(-(√(3) )/(2),(1)/(2) )`

`sin(x)=y`, so
`sin(x)=(1)/(2)`

`tan(x)=(y)/(x)`, so
`tan(x)=((1)/(2) )/(-(√(3) )/(2) )=-(1)/(√(3) )`

Now that we have sin, cos, and tan, we can just take the reciprocal of each of these to get our answers for csc, sec, and cot.

`csc(x)=(1)/(sin(x))`, so
`csc(x)=2`

`sec(x)=(1)/(cos(x))`, so
`sec(x)=-(2)/(√(3))`

`cot(x)=(1)/(tan(x))`, so
`cot(x)=-√(3)`