funny thing, teacher told me i need to write down process, so i can't calculator my way to correct answers anymore, fuckkkkkk

I wasn't talking about this homework set but rather I was
trying to give you some comfort for the future. What you've got is pretty easy anyways... all you have to do is memorize the unit circle and you've got it.
cos(60) = 1  2sin^2(30) // I'm assuming you meant sin^2 here
Well the cos(60) from the unit circle is 1/2, the sin(30) is also 1/2
1/2 = 1  2*(1/2)^2
1/2 = 1/2
or the one with cos(x) = 3/5
Since cosine is equal to adjacent/hypotenuse
adjacent = 3
hyp = 5
Applying pythagoream's theorem to a right triangle you get opposite to be 4
So the sin(x) = opposite/hyp = 4/5
tan(x) = opposite/adjacent = 4/3
The whole adj, hyp, and opp things you will just have to remember and later on down the road it becomes second nature
Cosine(theta) = adj/hyp = x/hyp
Sine(theta) = opp/hyp = y/hyp
Tangent(theta) = opp/adj = y/x
Since the sec, csc, and cot functions are just the inverse of their counterparts(and trust me rarely used except in computations), then you just invert the above fractions for their values... but really the easier way to think about it is sec(theta) = 1/cos(theta), and just let the algebra work it out.
So if you want the sec(60), then just take 1/cos(60) = 1/0.5 = 2