#1: What does it actually mean to verify a trigonometric function?
-Well before explaining how to solve a trig identity, I'll explain WHAT a trig identity is. A trigonometric identity is a "rule" that is always true no matter what. It's kind of like saying that pi= 3.14 or that the constant of gravity on Earth is 9.80 meters per second squared. So basically, in order to solve the identities, we need to use these rules in order to either simply the problem as much as possible, or just prove that the problem given to you is true (depending on what the problem asks for). That being said, there is always a way to solve the trigonometric functions, and you will not have a no solution. You can have one solution, more than one, but you will always have at least one.
#2: What tips and tricks have you found helpful?
-When solving the functions, I have found that it is always helpful to evaluate the problem before you start on it. Looking at what you have and think about what you can plug into the problem is a good way to start. Once you have a specific identity that you can plug in, you just plug them in and then you start to either combine, cancel, or multiply by the inverse, etc.
#3: Explain your thought process and steps you take in verifying a trig identity. Do not use a specific example, but speak in general terms of what you would do no matter what they give you?
-As mentioned in question #2, the first thing I do, is evaluate the problem. After I do this, I basically just tend to substitute in as much as possible, and then factor out. By doing this, I make my life easier, because I can just eliminate like terms. Then, you can usually re-substitute some of the identities and eliminate further. After this, you are usually done with the problem.
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