- #1

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## Homework Statement

sec 3[tex]\Theta[/tex] = 2

Find all solutions within 0 < [tex]\Theta[/tex] < 2[tex]\Pi[/tex]

## Homework Equations

none

## The Attempt at a Solution

I am having trouble "knowing" what angles satisfy sec = 2 within the interval.

I can find one... ArcCos 1/2 = 1.047... which I can guess is [tex]\Pi[/tex]/3.

The other is 4[tex]\Pi[/tex]/3, but I have NO idea how to get that angle.

I need both to format two different general formulas to get all possible answers, but I have no problem doing that. My problem is the first step, magically knowing the angles that satisfy sec = 2 within the interval. I can find one using inverse functions but I don't know how one comes to the second.