Question #b0a1e

1 Answer
Feb 1, 2018

#sec(tan^-1(-5/4))= -sqrt41/4# or #sec(tan^-1(-5/4))= sqrt41/4#

We cannot say which without being told whether the angle is in quadrant 2 or 4.

Explanation:

Use the identity #sec(theta)= +-sqrt(tan^2(theta)+1)# where #theta = tan^-1(-5/4)#

#sec(tan^-1(-5/4))= +-sqrt(tan^2(tan^-1(-5/4))+1)#

#sec(tan^-1(-5/4))= +-sqrt((-5/4)^2+1)#

#sec(tan^-1(-5/4))= +-sqrt((-5/4)^2+1)#

#sec(tan^-1(-5/4))= +-sqrt(25/16+1)#

#sec(tan^-1(-5/4))= +-sqrt(25/16+16/16)#

#sec(tan^-1(-5/4))= +-sqrt(41/16)#

#sec(tan^-1(-5/4))= +-sqrt41/4#