By this point you should be able to fill out a unit circle by heart and thats why one doesnt appear on this page.
1) CSC of 30°=2
*first remember that CSC is1/y
*go to 30°
*you see (√3/2,1/2)
*1/2 is the y value
*so you have 1/ 1/2
*when dividing you use the copy change flip rule
*copy the 1 so you have 1/1 change the sign to multiplication and flip the 1/2 to 2/1
*so you have 1/1 X 2/1
*simply multiply across
*you wind up with 2/1
*this can be written as 2
2) Sec of 11π/6=2√3/3
*find 11π/6
*you see ( √3/2, -1/2)
*remember that Sec is 1/x
*the x value is √3/2
*so you have 1/ √3/2
*again use the copy change flip rule
*copy the 1 so you have 1/1 change the sign to multiplication and flip the √3/2 to 2/√3
*so you have 1/1 X 2/√3
*multiply across to get 2/√3
*you can not have a square root in the denominator so multiply both the top and bottom by √3
*you are left with 2√3/3
3) Cot of π/3=look at the answers under "more"
1) CSC of 30°=2
*first remember that CSC is1/y
*go to 30°
*you see (√3/2,1/2)
*1/2 is the y value
*so you have 1/ 1/2
*when dividing you use the copy change flip rule
*copy the 1 so you have 1/1 change the sign to multiplication and flip the 1/2 to 2/1
*so you have 1/1 X 2/1
*simply multiply across
*you wind up with 2/1
*this can be written as 2
2) Sec of 11π/6=2√3/3
*find 11π/6
*you see ( √3/2, -1/2)
*remember that Sec is 1/x
*the x value is √3/2
*so you have 1/ √3/2
*again use the copy change flip rule
*copy the 1 so you have 1/1 change the sign to multiplication and flip the √3/2 to 2/√3
*so you have 1/1 X 2/√3
*multiply across to get 2/√3
*you can not have a square root in the denominator so multiply both the top and bottom by √3
*you are left with 2√3/3
3) Cot of π/3=look at the answers under "more"
