How do you evaluate tan(sec^-1 4)?

1 Answer
Bdub
Oct 13, 2016

tan(sec^-1 4)=sqrt15

Explanation:

tan(sec^-1 4)

The restriction for the range of sec^-1x is [0,pi],y!=pi/2 and since the argument is positive it means that our triangle is in quadrant I with the hypotenuse of 4 and adjacent of 1 and therefore using pythagorean theorem we have the opposite is sqrt15.

Therefore, the ratio for tangent from our triangle is
tan theta=o/a=sqrt15/1=sqrt15

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