How do you solve #sec (arctan 1.05)#?

1 Answer
Jun 29, 2016

#sec(arctan(1.05))=color(blue)(1.45)#

Explanation:

If #arctan(1.05)=theta#
then #tan(theta)=y/x=105/100# for a triangle with #theta# at the origin and X-axis leg #100# units long.

The hypotenuse of this triangle would have a length:
#color(white)("XXX")sqrt(x^2+y^2)=sqrt(105^2+100^2)=sqrt(21025)=145#

#sec(theta)=("hypotenuse")/x=145/100=1.45#