1. ## Solve for x

Hello,
I have summer homework and I'm very rusty on how to do some of the trigonometry problems as I haven't done anything like this in months. So if someone could even just point me in the right direction with this problem I would be very grateful. Thanks!

Solve for x, without a calculator: $sec^2\pi x = 4/\pi$

2. Are you sure it's not just

$\sec{(\pi x)} = \frac{4}{\pi}$? Because if so, remember that $\sec{X} = \frac{1}{\cos{X}}$, then you should be able to get an equation you recognise...

3. It's definitely $sec^2\pi x$. A lot of the problems on this assignment have seemed like they are "trick" problems already, designed to tempt kids into taking some kind of mathematically incorrect shortcut to solve, so I wouldn't put it past the teacher to throw the $^2$ in there just to see if someone takes the bait.

4. Originally Posted by Club

Solve for x, without a calculator: $sec^2\pi x = 4/\pi$
Without a calculator i get

$\sec^2\pi x = \frac{4}{\pi}$

$\sec\pi x = \sqrt{\frac{4}{\pi}}$

$\sec\pi x = \frac{2}{\sqrt{\pi}}$

$\frac{1}{\cos\pi x} = \frac{2}{\sqrt{\pi}}$

$\cos\pi x = \frac{\sqrt{\pi}}{2}$

$\pi x = \cos^{-1}\frac{\sqrt{\pi}}{2}$

$x =\frac{ \cos^{-1}\frac{\sqrt{\pi}}{2}}{\pi}$

5. Originally Posted by pickslides
Without a calculator i get

$\sec^2\pi x = \frac{4}{\pi}$

$\sec\pi x = \sqrt{\frac{4}{\pi}}$

$\sec\pi x = \frac{2}{\sqrt{\pi}}$

$\frac{1}{\cos\pi x} = \frac{2}{\sqrt{\pi}}$

$\cos\pi x = \frac{\sqrt{\pi}}{2}$

$\pi x = \cos^{-1}\frac{\sqrt{\pi}}{2}$

$x =\frac{ \cos^{-1}\frac{\sqrt{\pi}}{2}}{\pi}$
If it didn't have the power of 2, you would be able to find the exact value for $x$. With the power of 2, like Pickslides said, you can only get an "expression" for $x$.

6. Originally Posted by Prove It
If it didn't have the power of 2, you would be able to find the exact value for $x$. With the power of 2, like Pickslides said, you can only get an "expression" for $x$.
What do you mean exactly?

7. Never mind, I made a mistake...