Question

How do you determine all trigonometric ratios given `secθ=6/5`?

Answer 1

`sintheta=sqrt11/6,tantheta=sqrt11/5,costheta=5/6,`
`csctheta=(6sqrt11)/11, cottheta=(5sqrt11)/11`

Explanation:

If `sectheta = 6/5`
`costheta=1/(sectheta)=5/6`

`sin^2theta+cos^2theta=1`
`sintheta=sqrt(1-cos^2theta)=sqrt(1-(5/6)^2)=sqrt11/6`

`csctheta=1/sintheta=6/sqrt11=(6sqrt11)/11`

`1+tan^2theta=sec^2theta`
`tantheta=sqrt(sec^2theta-1)=sqrt((6/5)^2-1)=sqrt11/5`

`cottheta=1/tantheta=5/sqrt11=(5sqrt11)/11`