Mr. Cresswell said that he only wanted to move to Yuma if it was daylight for twelve hours for more than half of the year. According to my math, Mr. Cresswell should not move to Yuma. It would need to be twelve hours of daylight for seven months or more, but it's not.
After doing the trig verification project I learned that there are many different steps you can use to verify the problem. I also learned that there are ways to make it more difficult and sometimes it makes it easier to change it into sine and cosine in order to solve it. In the power-point it shows how to solve a problem step by step.
From doing this activity I learned how to use a unit circle to find the "Y" on the line. My big takeaways were being able to find the point on the unit circle without having them labeled. Also this activity really made me think about what I was doing. You couldn't just get an answer and think it's right, you have to check over your answer a couple times to make sure you did the right thing. Some connections I made during this activity was using the line with the labeled points to find the points on the unit circle, the line correlated with the circle. Not having Mr. Cresswell's assistance during the assessment was tough, not being able to ask him if the answer was right really made you rethink your work.
Using the table above I was able to make the graphs shown in the picture below. 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 would be 2pi. Secant Graph: The amplitude is none because they go on forever. The period is 2pi. Sine Graph: The amplitude is one and the period is 2pi. Cosecant Graph: The amplitude in the cosecant graph is none, they go on forever. The period is 2pi. Compare and Contrast The cosine and sine graphs look the same except the sine graph passes through (0, 0) and cosine has a point somewhere on the y-axis. Vertical Asymptote
For tangent and cotangent the vertical asymptote is at the end of each cycle. Cosecant has a vertical asymptote that occurs at pi and repeats every pi units. Secant has a vertical asymptote that occurs at pi/2 and repeats every pi units. |