Above is the work I did for the Cress and Little problem. I would advise Mr. Cresswell not to move to Yuma,Arizona because he wants the 12 hours of daylight to last more than half the year. In plugging the months into the problem I found out that it was only 6 months of 12 hours of daylight. He would want at least 7.
I enoyed this assignment. I liked it because it's a good feeling to solve one of these equations. Thye require a lot of work and smarts. The equation I made wasn't too hard. I knew that 1-cosine^2x is sin^2x so I split the sines apart and used the cosecantx and flipped it over. Thus I was able to take out one of the sines and then both sides were sinex. :)
I learned a lot from this activity we did. I learned how to use the unit circle to find the points on the line and to find the "y" from using the trig functions you are given. I actually enjoyed this activity and found out I know more than I could even imagine. Some connections I made were how to use the unit circle with trig functions. You can use the 30, 60, 90 and 45,45,90 triangles to find the points from the unit circle. Not having Mr. Cresswell to say that we got it right was really hard. It really made you second guess your answer. Towards the middle of it I became more confident about my answers and stopped second guessing myself.
Period and Amplitude
Tan Graph: The amplitude in the tangent graph is none, the graphs go on forever in both directions. The period of the graph is pi. Cotangent Graph: This graph has the same amplitude and period as tangent. Cosine Graph: The amplitude for cosine is one, and the period is 2pi. Secant Graph: The amplitude is none because they go on forever. The period is 2pi. Sine Graph: The amplitude for sine is 1. The period is 2pi. Cosecant Graph: The amplitude in the cosecant graph is none, they go on forever. The period is 2pi. Cosine and sine graphs are almost completely similar. Except the fact that the sine graph starts from the point (0,0) and goes up or down. In the cosine graph it starts at a point on the y-axis with the x at zero and either goes up or down. Asymptotes in cotangent and tangent are at the end of each cycle. Cosecant has a vertical asymptote that occurs at pi and repeats every time you hit a pi. Ex: 2pi, 3pi, 4pi... Secant has a vertical asymptote that happens at pi/2 and repeats every time you hit a pi unit. |