Question

Suppose that cos = 12/13 what is sin what is cos 2

Answer 1

First, some housekeeping:

cos = 12/13 is incomplete; "cos" must have an argument (input).

cos x = 12/13 is fine; here "cos" has the argument (input) x.

Given that cos x = 12/13, find sin x.  To do this, we'll need to find the length of the opposite side, given that the hypo length is 13 and the adj. side length is 12.

12^2 + opp^2 = 13^2, or            opp^2 = 169-144 = 25.

Then the opp side could be either 5 or -5.  Let's assume that it's +5, and that angle x is in the first quadrant.

Then sin x = opp / hyp  =  5/13   (answer)


cos 2 is an entirely different kind of problem.  Here you are told what the argument (input) to the cosine function is (it is 2, which here means 2 radians).

Using a calculator:  cos 2 = -0.416.  Note that the angle 2 rad is in QII, which is why the "adjacent side" is negative and also why the cos of 2 is negative.