Question

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

Answer 1

`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`