*EDIT~*

3.*14159*..

hey guys! It's mary here and as your scribe from yesterday, i'll be summarizing the *wonderful* moments of precal class...today. Sorry about leaving you with that cliff hanger last night. But as promised, i will finish the post.

For yesterday’s class, we learned..

~ What the sine and cos graphs looks like and why the way it does.

~ The

difference between the sine and cos graph, along

with the meaning of

**amplitude **and

**period**.

~ What a **sinusoidal axis** is.

~ The 4 ways you can alter a sine or cos graph. (Translations)

1a) **Sine Graph:** *wow, the image quality sucks. LOL bare with me!*

Okay, so in order to explain the graph, you must understand the unit circle. As you go around the unit circle, starting from zero(or 2/pi), the sin value

*increases than decreases*. The Sine

value goes from 0, 1, 0, -1, and back to 0 again as it makes it full circle. It has a

max value of 1 (when reaches /pi/2, and a min value of -1 (when reaches 3/pi/2).

Regarding the unit circle, the

sine graph displays the sine values as you travel around the unit circle, in a way where we can see that pattern. (of 0, 1, 0, -1, 0). This means the

y-axis on the graph

shows the sin value, while the

x-axis shows the distance traveled on the unit circle. (2/pi, /pi/2, /pi, 3/pi/2 etc).

Understanding this would come in handy when asked to draw a sine graph. 10 points for those who can understand the relationship!

(brownie points) if not, ask yourself this: "where does sin equal zero on the unit circle?" look at the sine graph, "where does sin equal 1 and -1 on the unit circle?" then look at the graph. Your answers should be the same as the answers on the graph. "zero,2/pi, /pi, /pi/2 and 3/pi/2". 1b) **Cosine Graph** Again, just like with the Sine Graph, the y-axis on the graph shows the cos value, while the x-axis shows the distance traveled on the unit circle.

2a)** Sine Graph vs. Cosine Graph**

The Sine Graphs and the Cosine Graphs are pretty much the same. The only difference is, cos is horizontally shifted, /pi/2 units to the left, on the x-axis, from the sine graph . This means, if you were to take a Sine Graph, and push it /pi/2 units to the left, you would have a Cos graph. And if you were to take a Cos Graph and pull it /pi/2 units to the right, you would have a Sine graph. "They are identical in amplitude, period, domain and range". I hope you guys can understand the picture below. I was trying to show you visually that the two graphs are /pi/2 units away from each other.

2b) **UH OH, new terms?!** *don't worry, i got this! ;)*

--------------------------------------

*mary says:*

whats **Period** and **Amplitude** again? -__-

*pj says:*

**Period **is how long it takes for 1 cycle to repeat

pj says:

**Amplitude** is the distance from the highest points to the average

*mary says:*

so 2pi?

pj says:

it's 2pi for the regular sine/cosine curve

-----------------------------------------

**Sinusoidal Axis: ***"Sinusoidal axis: is the line which passes directly through the center of the sin curve horizontally. This line is always parallel to the X axis if it is not the X axis to begin with."* The sinusoidal axis is used as a reference line when altering your sin or cos graph. Remember, its not actully part of the graph, so don't draw it on a test, unless told to.

**ALMOST DONE, STAY WITH ME GUYS!**

3a) **Translation:**

When graphing trig functions, there are four ways it can be altered. (from its regular form, sin(x) or cos(x).)

Shifting it up/down. (vertical shift)

Shifting it left/right. (horizontal shift)

Stretching it vertically.

Compressing it vertically.

**~Vertical shift (Shifting it up/down)** *this would go the same for cos and sine*

example:* (because its more effective than me blabbing away)* sin(x)-2

the negative 2 would move the max and min values, of the graph, **two units** **down**. Another way of looking at it, would be having the new sinusoidal axis *two units* down from the previous. In this case, the sinusoidal axis would go from 0 (x-axis) to -2. Then you would just draw the graph as you would from the new sinusoidal axis.

example: sin(x)+2

Just like before, but the positive 2 would move the max and min values, of the graph, **two units up**.

**~Horizontal shift(Shifting it left/right)** *this would go the same for cos and sine*

example: sin(x-2)

the negative 2 would move the of the graph, *two units right*, from the regular sin graph. Notice how i said right, not left.

example: sin(x+2)

the positive 2 would move the of the graph, two units left, from the regular sin graph.

**~Stretching&Compressing it**

example: sin(2x). sin(1/2x)

The 2 would compress the graph, twice as much. While the fraction, 1/2, would stretch it twice as much.

**3b) Translation order; DABC!**

Most of the time, you will be faced with a combination of these translations. (vertical/horizontal shift, compress/stretch). And there is a order you go by, when you have to draw them. D A B C

From AsinB(x+C)+D or AsinB(x-C)+D, you would use DABC. Meaning you would do the vertical shifts first, since D is first in order.

*Okay, enough of the snore-fest!*

**IMPORTANT NOTICES!**

1) Mr. K will not be in class for the rest of this week, and the following week after. Reason: because of a family emergency. But

*show no fear,*(that one was for you

pj!), Mr. k had said he’ll keep in touch with us through the blog, and

I'm sure everything will work out with Mr. K's situation.

2) Also, there is still an

*unit test* on Friday,

FEBRUARY 20

th. Study hard and good luck :D

Resources:

http://www.cbv.ns.ca/mathhelp/P66.htmhttp://www.clarku.edu/~djoyce/trig/http://www.fooplot.com/

Next scribe will be laika~