# Math Help - Please find exact value without calculator

1. ## Please find exact value without calculator

Please explain how to find exact value without the calculator

sec ( tan^-1 5)

Thank you

2. Hello,
Originally Posted by oceanmd
Please explain how to find exact value without the calculator

sec ( tan^-1 5)

Thank you
Recall that $1+\tan^2u=\sec^2u$

So $\sec^2(\tan^{-1}(5))=1+[\tan(\tan^{-1}(5))]^2=1+(5)^2=6$

Now you have to see in which quadrant $\tan^{-1}(5)$ is in order to get the sign of $\sec(\tan^{-1}(5))$

Looks good to you ?

3. Originally Posted by oceanmd
Please explain how to find exact value without the calculator

sec ( tan^-1 5)

Thank you

Draw a triangle...

Then use the pythagorean theorem to find the unkown sides.

Then use the definiton of Sec to find the wanted ratio.

4. TheEmptySet,

Thank you very much.