Basic Trigonometry Question

I am so confused on some of this stuff. I am in algebra 2 and we are doing trigonometry, it's all very basic so please don't go in depth you're only going to confuse me more. I need help with this type of problem, please show all of your work. It says to find the exact values of the cosine and sine of each angle. (This is when you have to use like the square root of 3 and 1/2 of the hypotenuse, not just plugging in 30 degrees in your calculator).

So the problems are find the exact value of the cosine and sine of -60 Degrees

As well as 225 Degrees. I know this one is a 45 45 angle but I have no idea what to do. Any help would be much appreciated.

You're probably not going to find the answer you want here, because you haven't explained what method they want you to use. There are many, many ways to get the answer to this problem. Here's one: in general, you need to memorize the following:

for sine:

sin(0) = sqrt(0)/2 = 0
sin(30) = sqrt(1)/2 = 1/2
sin(45) = sqrt(2)/2 = sqrt(2)/2
sin(60) = sqrt(3)/2 = sqrt(3)/2
sin(90) = sqrt(4)/2 = 1

for cosine:

cos(0) = sqrt(4)/2 = 1
cos(30) = sqrt(3)/2 = sqrt(3)/2
cos(45) = sqrt(2)/2 = sqrt(2)/2
cos(60) = sqrt(1)/2 = 1/2
cos(90) = sqrt(0)/2 = 0

Hopefully you see the pattern there and why it should be easy to memorize.

Now, you also need to know that all trig functions are positive in quadrant 1, only sine is positive in quadrant 2, only tangent is positive in quadrant 3 and only cosine is positive in quadrant 4.

sin(60) = sqrt(3)/2, then make it negative since we're in quadrant 4. cos(60) = 1/2, keep it positive since we're in quadrant 4.

sin(-60) = -sqrt(3)/2, cos(-60) = 1/2

225 is 45 degrees into quadrant 3. sin(45) and cos(45) are both sqrt(2)/2. Only tangent is positive in quadrant 3, so make them both negative.

sin(225) = -sqrt(2)/2, cos(225) = -sqrt(2)/2