Question

How do you find all six trigonometric function of `theta` if the point `(sqrt3,-1)` is on the terminal side of `theta`?

Answer 1

Given: `(x,y) = (sqrt3,-1)`

Compute r:

#r = sqrt(x^2+y^2)

`r = sqrt((sqrt3)^2+(-1)^2)`

`r = sqrt(4)`

`r = 2`

`sin(theta) = y/r`

`sin(theta) = -1/2" [1]"`

`cos(theta) = x/r`

`cos(theta) = sqrt3/2" [2]"`

`csc(theta) = 1/sin(theta)`

`csc(theta) = -2" [3]"`

`sec(theta) = 1/cos(theta)`

`sec(theta) = (2sqrt3)/3" [4]"`

`tan(theta) = sin(theta)sec(theta)`

`tan(theta) = -sqrt3/3" [5]"`

`cot(theta) = 1/tan(theta)`

`cot(theta) = -sqrt3" [6]"`