Question

Find the exact value of: sec -22π/3

I need to show work help please

Answer 1

Well lets write it as

\[\large sec(-22\times \frac{\pi}{3})\]

Now consider going around the unit circle as 2pi

So going around an around it will eventually lead us to going 22pi around

Which (since we are back where we started) wil leave us with

\[\large sec(-\frac{\pi}{3})\]

And evaluating that, we will have

\[\large \sec(60^\circ)\]

\[\large sec60^\circ = \frac{1}{cos} = -\frac{1}{cos60^\circ} = -\frac{1}{\frac{1}{2}} = -\frac{2}{1} = -2\]