Really, Davis, if you cannot do a, b, and d, you are in the wrong class.
Show me those three, then we can talk about Right Trangles and the Pythagorean Theorem and tackle c.
Can you do a, b, and d? Those just require you to use a basic property of inverse functions that you should have learned in algebra: if and are inverses of each other, then . Of course, the trigonometric functions aren't actually invertible unless you restrict their domain, so you need to be careful when applying this property that the angle falls into the range of the inverse function. Otherwise, you would have to match the angle to the corresponding one in the range: for example.
For c, it is helpful to draw a triangle.
This is code for the following speech...
You have missed something fundamental. It is possible you have missed important prerequisites before you ventured into trigonometry. The concept of the inverse function should have been drilled into your head at least 3 times before you got to this class on trigonometry. There should have been whole units on it in Pre-Algebra, Algebra I, and Algebra II.
There is no personal insult, here. There is only the gravest of warnings that you probably are not missing just a little hint or two. If you are to survive this course, you absolutely MUST step it up a little. If we wait around for you to realize the difficulty involved, it may be too late. Someone with enough compassion and honesty should step forward and offer a solemn warning that things are not as they should be.
It just seems to me to be so much easier to use the shorter language and hope offense will be taken only where it is intended. In this case, there is none intended or expressed.