how do you find cosine x if secant x is equal to radical 5 ?``

Expert Answers
lemjay eNotes educator| Certified Educator

`secx=sqrt5`

`cosx=?`

Take note that the reciprocal of cosine is secant.

`sec theta =1/costheta`

And the reciprocal of secant is cosine.

`cos theta =1/sec theta`

So to solve for the value of cosine given the value of secant, apply the formula above.

Plug-in `secx=sqrt5` .

`cosx=1/secx`

`cosx =1/sqrt5`

Since there is a square root at the denominator, we have to rationalize the denominator to simplify it.

`cosx=1/sqrt5*sqrt5/sqrt5`

`cosx=sqrt5/5`

Thus, when `secx=sqrt5` , the value of cos x is `sqrt5/5` .