Well, it looks like the first problem is just a case of applying the definitions of the five listed trigonometric functions. My guess is that theta is meant to refer to the angle, even though in the picture it appears to be labeling the third side of the triangle. So, how far have you gotten in apply said definitions? As a hint, I find the mnemonic device "SOH CAH TOA" to be helpful. The second problem's tricky at first, but I'd start by using the following identity:
\(\displaystyle sin(s+t)=cos(s) \cdot sin(t)+cos(t) \cdot sin(s)\)
Then, you can convert the inverse sines to inverse cosines as necessary. Try drawing a triangle and using your mnemonic if you're uncertain as to how that would work.
Problem three is a case of using the results from problem one and plugging in specific values. How far did you get in that process?
For problem four, draw a diagram. Based on the fact that you're studying trig functions, you know you'll want to draw a triangle. Using the information given, which two sides of the triangle do you think you can label? Then use the Pythagorean theorem to find the third side. Now you can use the mnemonic to find any of the trig functions of your angle of elevation (call it theta). Can you use this new information to find the value of theta?
Finally, for problem five, I'd note that, as their name suggests, the inverse trig functions are, well, the inverse of the regular trig functions. Recall back to algebra. Let's say you have a function f(x) and it's inverse f-1(x). If you evaluate f(f-1(x)), what do you get? What does that tell you about what might happen if you take the sine of a inverse sine of a number? You can also use this information as a big hint for problem two if you're still stuck there.
