Precal Help?

[94tank]

I'm working on the following problem:
cos4x = -√3/2

but I don't see why the book listed the following solutions.
{5π/24, 7π/24, 17π/24, 19π/24, 29π/24, 31π/24, 41π/24, 43π/24}

When I change n to 1 I get 11pi/24. I'm completely stuck with this problem. Perhaps I'm not understanding the concept?

 

[Ishuda]

I'm working on the following problem:
cos4x = -√3/2

but I don't see why the book listed the following solutions.
{5π/24, 7π/24, 17π/24, 19π/24, 29π/24, 31π/24, 41π/24, 43π/24}

When I change n to 1 I get 11pi/24. I'm completely stuck with this problem. Perhaps I'm not understanding the concept?

What do you mean 'When I change n to 1'?

HINT: Suppose sin(x) = \(\displaystyle \dfrac{\sqrt{2}}{2}\). Then
x = \(\displaystyle \dfrac{\pi}{4}\, +\, 2\, n\, \pi;\, n=0,\, \pm1,\, \pm2,\, \pm3\, ...\),
OR
x = \(\displaystyle \dfrac{3\pi}{4}\, +\, 2\, n\, \pi;\, n=0,\, \pm1,\, \pm2,\, \pm3\, ...\),
That is, given a y, \(\displaystyle -1\, \lt\, y\, \lt\, 1\), the sine and cosine take on that value of y twice each cycle.

 

[94tank]

What do you mean 'When I change n to 1'?

HINT: Suppose sin(x) = \(\displaystyle \dfrac{\sqrt{2}}{2}\). Then
x = \(\displaystyle \dfrac{\pi}{4}\, +\, 2\, n\, \pi;\, n=0,\, \pm1,\, \pm2,\, \pm3\, ...\),
OR
x = \(\displaystyle \dfrac{3\pi}{4}\, +\, 2\, n\, \pi;\, n=0,\, \pm1,\, \pm2,\, \pm3\, ...\),
That is, given a y, \(\displaystyle -1\, \lt\, y\, \lt\, 1\), the sine and cosine take on that value of y twice each cycle.

"When I change n to 1", I meant when I plug in 1.

The problem I had was that I wasn't including the period formula. 2pi/|b|

Thanks for your insight though.