Hey everybody! This is my first ever post on this blog ever, or any blog for that matter, so I don't exactly know how to start. I guess I could start by saying how much I love this class so far, and then progress into what we learned in the class so far, which is the almighty unit circle.
Throughout our unit of the unit circle, I haven't quite encountered any insurmountable roadblocks in terms of difficulty comprehending anything. Overall I understood everything, except for those classes which I missed (for worthy reasons of course), but I did manage to catch up thanks to the oh so helpful podcast. Homework was another big thing, and I really am glad that for a change, I am fully completing it and am not procrastinating in doing so. I really hope the rest of you have been doing your homework too. I think it really helps with understanding each aspect of the concept further and helps with subtlizing each problem so that new problems of a similar nature won't present as much tribulation as it could have. And seeing as our test is coming up tomorrow, I think the homework Mr. K has given us can provide us with much practice solving problems that will probably be on the test. I think that I, as I advise the rest of the class to do, am going to utilize these questions to us as help to prepare for the gruesome fear-inducing test tomorrow.
But try not to forget all the mnemonics and tips Mr. K has given us to help us remember certain segments of the unit, such as:
- The exact values of the functions sin and cos found on the unit circle follow the pattern of 1, √2, √3 (all of which are over 2). Visualize where the angle is found on the unit circle, then use this to help imagine what the exact co-ordinates of that point are.
- The exact values of the tan function (sinx/cosx) follows a pattern of 1/√3 ,1, √3. It ascends along this pattern as it travels away from the x-axis, and reaches undefined at the y-axis, then descends back down this pattern until it reaches the x-axis again. The same goes for underneath the x-axis, but remember that tan is negative in quadrants 2 and 4.
- F(x)=AsinB(x-C)+D F(x)=AcosB(x-C)+D
Remember DABC to remember the order when graphing a trigonometric function.
D -> A - > B -> C
Start by visualizing or drawing in(using a dotted line) the D parameter, then A, subsequently determine B by using:
B= 2Π /Period
Use this value to scale the x-axis. Once all of those are done, C (the phase shift) will be used to show draw how much the graph is shifted horizontally.
- Think proportionally! It's a great way to think and a logical method to solving problems, and is accurate and simple as well.
Well, sorry if I made this BOB too long, I just got carried away. =/ Well, I guess I'll end this off here by saying that I really like this class, and I'm glad I'm understanding everything perfectly so far (despite what the recent quiz might show). So, I wish everyone good luck on their test tomorrow, and don't forget to study!