Is this right? (trig equation)

[Byrgg]

It's set up like this and you have to solve for all possible angles:

-360 degrees <= theta <= 360 degrees

8cos ^ 2 theta + 7cos theta - 1 = 0

(my work)

(8cos - 1)(cos theta + 1) = 0

8cos theta - 1 = 0
8cos theta = 1
cos theta = 1/8
theta = 1/8 cos ^ -1

theta = 83 degrees
= -83 degrees
= 277 degrees
= -277 degrees

OR

cos theta + 1 = 0
cos theta = -1
theta = -1cos ^ -1

theta = 180 degrees
= -180 degrees

The back of the textbook has only the answers before my "OR", they do not show the possible 180 and -180 degrees that I calculated, did they just forget or did I mess something up?

 

[Doc Al]

They must have left them out--your answers are correct. You can verify that those answers are correct by plugging them back into the original equation.

 

[Byrgg]

Ok thanks for your time, it not's the first time I've encountered incorrect(or in this case exclusive) answers in a textbook, just wanted to make sure.

 

[Byrgg]

Actually there's one more, would you mind helping me?

 

[Doc Al]

Let's have it.

 

[Byrgg]

Never mind I just figured it out, I accidentally wrote 4/2 * 1 = 1 instead of 2

I got the right answer after that correction, thanks anyways.