Question

How do you find the values of the six trigonometric functions of an angle in standard position if a point with `(-8, -15)` has on its terminal side?

Answer 1

Given: `(x,y)`
Compute `r=sqrt(x^2+y^2)`
`sin(theta)=y/r`
`csc(theta)=r/y`
`cos(theta)=x/r`
`sec(theta)=r/x`
`tan(theta)=y/x`
`cot(theta)=x/y`

Explanation:

Compute r:

`r = sqrt((-8)^2+(-15)^2)`

`r = 17`

`sin(theta)=-15/17`

`csc(theta)=-17/15`

`cos(theta)=-8/17`

`sec(theta)=-17/8`

`tan(theta)=15/8`

`cot(theta)=8/15`