Question

Find the value of each of the trigonometric functions of theta? sec theta=11, tan theta >0

Answer 1

`sintheta=(2sqrt30)/11`; `costheta=1/11`, `tantheta=2sqrt30`
`cottheta=1/(2sqrt30)`, `sectheta=11` and `csctheta=11/(2sqrt30)`

Explanation:

As `secteta=11` and `tantheta>0`, both ratios being positive `theta` lies in `Q1` and all trigonometric ratios are positive.

As `tan^2theta=sec^2theta-1`

`tantheta=sqrt(sec^2theta-1)=sqrt(11^2-1)=sqrt120=2sqrt30`

and `cottheta=1/(2sqrt30)`

As `sectheta=11`, we have `costheta=1/sectheta=1/11`

Now `sintheta=tanthetaxxcostheta=2sqrt30xx1/11=(2sqrt30)/11`

and `csctheta=11/(2sqrt30)`