Reflection #1: Unit Q - Verifying Trig Identities

1.) To verify a trig identity, it means both sides of an equation has to equal to each other. This requires simplification on the left side only, as the right side is not to be touched. In most or in all cases, the right side is already simplified to one or two trig identities, so rewriting it would create complications and more work. Throughout the verification and simplification, identities (definition from Mrs. Kirch: proven facts and formulas that are always true) are used for substitution, canceling, etc. The relations of the 11 identities all have some sort of pattern that go/relate with one another.

2.) There are a few tips and trick to verifying a trig identity. If the problem looks simple, start by checking if an identity would work. Usually from there, one identity will lead to another and trig functions will start canceling out perfectly. But if the problem is more complex, like those in Concept 5, the process is a bit different. For fractions, separation might work best but in some cases multiplying the conjugate works as well. In fractions, mainly, the problem looks most complicated, however one should not be afraid them as the fraction will simplify and decrease its size along the way. In other situations and problems, factoring a common multiple might help, while in the other hand powering up/down will also do the trick. Trig identities are also usually found where there is any addition/subtraction of number values. A main thing to remember is that one CANNOT divide by a trig function.   

3) When a trig identity is given to be verified, I feel less tense as the answer is technically already given but needs to be simplified/proven. I always look at the right side at the "answer" and start thinking how I would want to rearrange the problem to get there [to the answer]. I usually start simple by checking if an identity can be substituted in order to cancel out. I also search for some sort of relation that holds the problem together and that can be used to break it down. I prefer factoring since in many cases it would simplify to a trig identity. I try avoiding multiplying binomials/conjugates, squaring binomials, etc as it involves more work and can have several sections were mistakes can be made.