Reflection #1: Unit Q: Verifying Trig Identities

1. What does it actually mean to verify a trig identity?
To verify a trig identity means to confirm that both sides of the equation are equal to one another, or that the equation is true. We do this by using different identities that we need to prove the equations that we are given.

2. What tips and tricks have you found helpful?
I have found that converting every trig function to sine and cosine helps when verifying or simplifying. Other tricks that I have found helpful is to split fractions that have monomial denominators to simplify even further or to combine fractions with a binomial denominator. It also helps me to look for greatest common factors to factor out of polynomials in the equation and then possibly use Pythagorean identities to simplify.

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.
My first step is look for any trig functions that can be converted into sine and cosine, as those are the easiest to work with. If the trig functions are squared in the equation, I would also look for the trigonometric pairs that go with each other: sine and cosine, cosecant and cotangent, and tangent and secant. If I have those, then I would use them instead of converting. I might change one of the trig functions to the other using a Pythagorean identity. However, if I do not have any trig functions squared, then converting everything to sine and cosine is the simplest way.

If I have a fraction, I will look for two things. One of them is if I can multiply the numerator and denominator by the denominator's conjugate. This will work only if I have a binomial denominator and if I can't cancel anything out on the top and bottom anymore. After I multiply in the conjugate, I most likely will end up with a Pythagorean identity, so I can substitute in one trig function and split the fraction if I have to--only if I cannot simplify the numerator and denominator of the fraction first.