Question

The point P on the unit circle that corresponds to a real number t is [5/7, 2 square root 6/7] how do you find csc(t)?

Answer 1

`csc t = (7sqrt6)/12`

Explanation:

Coordinates of P:
`P (x = 5/7, y = (2sqrt6)/7)`
we have:
`tan t = y/x = ((2sqrt6)/7)(7/5) = (2sqrt6)/5`
`cot t = 1/(tan t) = 5/(2sqrt6)`
Apply the formula:
`csc^2 t = 1 + cot^2 t = 1 + 25/24 = 49/24`
`csc t = 7/(2sqrt6)` (because t is in Quadrant 1)
`csc t = (7sqrt6)/12`