Review+Day+1

Today in class, we mainly reviewed for the test that is coming up on Monday. In our period, someone had a question on # 19 from section 1.13. The question read:

Find all the values of //t// between 0 and 120 that are solutions to the equation math 36cos(\frac{2\pi }{60}(t-5))+39 = 12

$

First, we noted that the reason that the equation has the unsimplified $ \frac{2\pi }{60} $ instead of the simplified $ \frac{\pi }{30} $ is because it is easier to determine what the period is when the equation is in this form. Using $ \frac{2\pi }{b} $, we can tell that b, or 60, is the period in this case.

Next, we solved following these steps:

$$

36cos(\tfrac{2\pi }{60}(t-5))+39 = 12

36cos(\tfrac{2\pi }{60}(t-5))= -27

cos(\tfrac{2\pi }{60} (t-5))=-\tfrac{3}{4}

\tfrac{2\pi }{60} (t-5)=cos^{-1}(-\tfrac{3}{4})=2.42 + 2\pi k, -2.42 +2\pi k

t-5= \tfrac{60}{2\pi} \ast 2.42 +60k, -\tfrac{60}{2\pi} \ast -2.42 +60k

t-5=23.1 +60k, -23.1+60k

t=28.1+60k, -18.1 +60k

Then, we assumed that k was 0, 1, or 2. We plugged in these values and got that

t = 28.1, 88.1, 41.9, 101.9

$ math

Next, we discussed what amplitude can be found.

This image was obtained from wikipedia commons. In this image, the amplitude is y and the period is. Finally, we went over the [|"It's Time to Study"] handout from the start of the year, now that the information is applicable. To study effectively, we can:
 * go over old homeworks and make sure that we know exactly what we got wrong and why.
 * look at the class wiki to review or go over our own class notes
 * use the online practice at PHSchools.com, using the codes available in our book.
 * use discretion with these questions though, all of them are multiple choice and may not be the best quality of questions to review with.
 * use the chapter test and review from the book (check the answers from the sheet given out in class)
 * all Check Your Understanding problems' answers are in the back of the book, making them easy to check.