Reflection:
1. To verify a trig function really means that you are checking to make sure that whatever the equation says is true. You are basically solving the trig function and if all goes well it should be the same single trig function that is on the other side of the equal side. To verify means to go through the problem step by step and use the identities to replace functions and cancel out other functions and in the end (a majority of the time) get a single trig function. If you worked each step right and paid attention to all the details the left and right side of the equations should match up. To verify means to check and that is what you are doing. It is like when you are plugging x back into an equation, you are verifying (checking) to make sure that it is true. Try not to complicate it. You are reducing, replacing, and canceling out trig functions on the left side of the equal sign to make sure it matches the right side.
2. As I have gone through this unit I have found that it is always easy to take some deep breaths and then begin in on the problem. You always have to try, even if you think that it is too hard and you cannot do it, you still need to try. Sometimes when you try you can get the answer or a lead in the right direction. It is always good to try. You will never succeed if you don't try, if all you can say is you can't. Another thing that I find helpful is to try to make it so that the answer is in terms that you understand or make things into identities to shrink the problem down. Always make it smaller. It can help you understand it, to take it in and relax. Also try and get rid of the fractions on fractions. This can lead to ratios canceling out and your life getting a little bit easier. Always try to make the problem something that you can look at and understand. I always find it easier when you can break the problem up and just look at it section by section and then look at the big picture. It is always easier to make the problem a little bit more manageable Remember that it is always better to try and fail than to never try at all. Oh one more thing. Never forget your theta or x or whatever the variable is (they are very important to the overall understanding of the problem). Good luck.
3. When I first see a problem I like to take a breath and see what type of problem it is (verification or simplifying or solving). From there I take it step by step. I see if I can make anything cancel out easily. If that does not work and I feel like I am stuck I change the trig functions to sin and cos because it is easier to work with. With that it is easier to try and figure things out. We then have the ability to factor or multiply. With that it is just easier to go about working with it. If it is a large one, then we just have to look at it in pieces. Make it so that it is easy to work with. I don't really know if my thought process is clear, but I just look and see the best route. The best replacements and cancelations. It is easier for me to work things out when they are smaller and a little broken down. It is easier to take it all in when it is in chunks. I just look for all the simple ways to get it done. That is my plan of action. Not the clearest or the best, but it works for me.
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