Well when you want to isolate a variable that's inside a trig function, you just take theinversetrig function.

For instance, with the first problem:

.

We take of both sides (sometimes, is written and pronounced ). Get:

, so resolving the left side gives:

.

We now have to figure out what is. Well it's like asking "what angle in a right triangle gives a ratio of opposite side over adjacent side equal to 1?" It should be obvious that a 45-45-90 triangle passes this test, so resolves to , or . However, there may be more answers. Notice that works as well. In fact, for any integern, , so could be any of these.

We take this info and go back to our equation:

. So:

. Then:

.

All right, but you were given a restriction of possible values, .

So we want to figure out the only values ofnthat make our solution valid. ,

,

,

.

Soncould only be 0,1,2,3,4,5,6, or 7.