Question

Given `Sec θ=9`, what are the other trig functions given tanθ<0?

Answer 1

`costheta=1/9`
`sintheta=sqrt80/9`
`cosectheta=9/sqrt80`
`tantheta=sqrt80`
`cottheta=1/sqrt80`

Explanation:

`sectheta=9`
`costheta=1/sectheta=1/9`=======Ans `1`

`sintheta=sqrt(1-cos^2theta)`
or
`sintheta=sqrt(1-(1/9)^2`
or
`sintheta=sqrt(1-1/81`
or
`sintheta=sqrt((81-1)/81)`
or
`sintheta=sqrt(80/81)`
or
`sintheta=sqrt80/9`==========Ans `2`
`cosectheta=1/sintheta=9/sqrt80`=========Ans `3`
`tantheta=sintheta/costheta=sqrt(80)/9-:(1/9)=sqrt80`=======Ans `4`

`cottheta=1/tantheta=1/sqrt80`==========Ans `5`