Please explain how to find exact value without the calculator

sec ( tan^-1 5)

Thank you

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- Apr 20th 2009, 06:38 AMoceanmdPlease 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 AMMoo
Hello,

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 AMTheEmptySet

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 AMoceanmd
TheEmptySet,

Thank you very much.