Question

How do you find the six trigonometric functions of `(-3pi)/2` degrees?

Answer 1

If you really* meant degrees you will need to use a calculator;
if you meant `(-3pi)/2` radians**, note that `(-3pi)/2` is equivalent to `pi/2` and use the standard trig values.

Explanation:

Degrees
`(-3pi)/2` degrees `= -0.08225` degrees
from there you can use a calculator to determine (for example)
`color(white)("XXXX")` `sin(-0.08225^o) = -0.00144`
`color(white)("XXXX")` `color(white)("XXXX")`(I know of no other way to find this value)

Radians
`(-3pi)/2 = pi/2`

Using the standard trigonometric ratios:
`sin((-3pi)/2) = sin(pi/2) = 1` `color(white)("XXXX")` `csc((-3pi)/2) = 1/sin((-3pi)/2) = 1`

`cos((-3pi)/2) = cos(pi/2) = 0` `color(white)("XXXX")` `sec((-3pi)/2) = 1/cos((-3pi)/2) = "undefined"`

`tan((-3pi)/2) = sin(pi/2)/cos(pi/2) = "undefined"` `color(white)("XXXX")` `cot((-3pi)/2) = cos(pi/2)/sin(pi/2) = 0`