Reflection #1: Unit Q: Verifying Trig Identities

1. The meaning of verifying a trig identity is to prove that the equation is true and we do this by showing that both sides are equal to each other.

2. Tips and tricks that I found helpful are to try to always change the identities to sin(x) and cos(x) when possible. Another tip I would use is to try to convert the equation into a Pythagorean identity when it applies. Another important tip is to NEVER TOUCH THE RIGHT SIDE OF THE EQUATION! Always start with the left because you are verifying if it does equal to the right side. We love having our equations to have squares, so if your answers can not go further, you then can square both sides to get a Pythagorean identity out of it. A very important tip to always do when squaring both sides is to check your answer in the end to make sure it works, because the answer can be extraneous. A trick I would give you is to use the "u-substitution" because it is helpful when factoring trigonometric expressions. And it makes it easier during the factoring process because after you factor, you just plug everything back in! So easy!

3. My thought process through the steps when verifying trig identities is to look at the equation in general. I first check to see if we want the left and right side of the equation to equal to each other or if we are looking for a specific answer (degrees/radians). If we are looking for an answer, than the first thing I would do is to try to change the equation into sin(x) and cos(x). I would then look for a Pythagorean identity in order to have the same identity throughout the problem. I would also check to see what quadrants it lands on because it helps us determine where our answer will lay in. I would also see if I can use the "u-substitution" or "m-substitution" to make my life easier. If we were looking to see if the equations on both sides equal to each other, I would start with the left side and leave the right side alone and then bring it back down when in the end. I will also see if I can separate the equation, get a common denominator, FOIL, combine, cancel, replace, convert, or change identities. I need to have my options open to how I want to approach the problem. I also use my right side equation as guidance to where I want to be. My right side equation can tell me if a should combine and cancel or change and convert to a different Pythagorean identity. What I recommend to do is to look at the equation first and analyze the starting point and then see where we want to end. In my opinion, that is the key. Analyze the equation before making a move.