# Please find exact value without calculator

• Apr 20th 2009, 06:38 AM
oceanmd
Please find exact value without calculator
Please explain how to find exact value without the calculator

sec ( tan^-1 5)

Thank you
• Apr 20th 2009, 06:41 AM
Moo
Hello,
Quote:

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

sec ( tan^-1 5)

Thank you

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

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

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

Looks good to you ?
• Apr 20th 2009, 06:47 AM
TheEmptySet
Quote:

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

sec ( tan^-1 5)

Thank you

Draw a triangle...

Attachment 11011

Then use the pythagorean theorem to find the unkown sides.

Then use the definiton of Sec to find the wanted ratio.
• Apr 21st 2009, 06:45 AM
oceanmd
TheEmptySet,

Thank you very much.