Reflection #1 - Unit Q: Verifying Trig Identities

I - What does it actually mean to verify a trig identity? 

Verifying a trig identity is one of the easier things to do throughout this concept. What it means, is that you have to take the given problem, and simplify it so that the left side is equal to the right side. In other words, you verify that one side equals the other even if they are formatted differently. 

II - What tips and tricks have you found helpful?

Starting off this unit, you will most likely feel extremely confused and probably won't want to touch an identity. It gets easier! Sort of... Something that really helps get problems done quickly is knowing all of your identities (ratio, reciprocal, and Pythagorean)! Knowing identities by heart will speed up the process of simplifying as you know what you want to get to in order to solve the problem. This will also prevent you from having to search through the SSS to find ways to work out the problems. One of the most important tips any Math Analysis student could give incoming identity solvers is to not give up! It is obvious that this is one, if not the most, of the more challenging units of the year; that just means that you need to push through it to succeed. Study, do your PQ's, and practice in order to do well on the test. As far as tricks go, don't be afraid of pulling out a GCF, substituting an identity, or playing with fractions! These steps will help you conquer the beast that is mathematical identities. 

III - Explain your thought process and steps you take in verifying a trig identity.

As soon as I look at my problem, the first thing I need to do is see what I'm working with. "Do I need to verify or solve?" The next step would be to then see if I should be pulling out a factor from the problem. If i need to, then I proceed to pull out the factor and attempt to set the problem equal to zero so that I can use the Zero Product Property. The next step would be to go on to see if anything can be simplified into a Pythagorean Identity. If something can be, then I go ahead and substitute one for the other. This may help us cancel out some parts of our problem. Depending on the problem, this may be enough to find your answer. However, dealing with fractions can cause some difficulty. When I come across fractions, I do the same steps as earlier, but then also take into the account the denominator. If there is a binomial on the bottom, we can multiply by the conjugate in an attempt to make our fractions a little easier to work with. If there is a monomial in the denominator, we can go ahead and split the fraction into two separate fractions. From these two steps, we can go on to factor our problem! These should all be accompanied by and explanation on the right hand side of the paper! With that, good luck to the future math analysis students!