Kaitlyn's Blog #4

I am going to explain Chapter 8, Sections 1 and 2. This chapter was actually pretty easy for me. I understood it more quickly than i understood chapter 7.



8-1



In this section, we are solving for (theta) by getting the trig function by itself and then taking the inverse of it. An inverse must have 2 answers, with exceptions. Here are the formulas to getting the numbers in the different quadrants:

Q2: make negative and add 180

Q3: add 180

Q4: make negative and add 360



Ex: 2sinx=1 -- simplifies to sinx=1/2

-Take the inverse of this -- x=sin^-1 (1/2) = 30



- on the unit circle, this would be in the 1st quadrant. Since sin is positive in the first and second quadrant, you want to get 30 in those quadrants (30 is already in the first so just solve for the second). -30+180=150



- Your answers are: 30 and 150





8-2

In this section, you are graphing the period changes of sine and cosine

- y=AsinBx or y=AcosBx

- A=amplitude

- 2(pi)/B=period

Steps to graphing with a period change:

- Take all 5 points (0, (pi)/2, (pi), 3(pi)/2, 2(pi))

-Divide by B

-Sketch your graph

Ex: y=10sin5x

amp: 10 period: 2(pi)/5

1. 0/5= 0
2. (pi)/2/5= (pi)/10
3. (pi)/5= (pi)/5
4. 3(pi)/2/5= 3(pi)/10
5. 2(pi)/5= 2(pi)/5

(Then you would graph these points. The graph will come out to be wavy and since it is sin, it will pass through the origin.)