Question

Let `theta` be an angle in quadrant II such that `sintheta = 5/6`. What are the exact values of `sec theta` and `tan theta`?

Answer 1

`-6/sqrt11,-5/sqrt11`

Explanation:

`• costheta=+-sqrt(1-sin^2theta)`

`color(white)(xxxxx)=-sqrt(1-(5/6)^2)larr" negative in quadrant 11"`

`color(white)(xxxxx)=-sqrt(11/36)=-sqrt11/6`

`• sectheta=1/costheta=-6/sqrt11`

`• tantheta=sintheta/costheta`

`color(white)(xxxxx)=5/6xx-6/sqrt11=-5/sqrt11`