Thursday, September 20, 2007

CIRCULAR FUNCTIONS

Hello fellow classmates,
I am SAM and I'll be your scribe for the day. First thing we did was answer Mr. K's question. He asked us individually if we had read his post, Students Made This. Fortunately enough, everyone did. So expect a chat box and a walkie-talkie device thingy soon. Right after that we jumped right into math. We started off with the equation y= Cos2x, which we had to graph.



STEP 1:
check if parameter D is present.

STEP 2: check if parameter A is present.
STEP 3: check if parameter B is present. Since B is 2 that means that the period has changed. and to find the period you divide 2π/ B. So 2π/ 2 = π, the period is π. That means that there are now two waves between 0 and 2π.
STEP 4: check if parameter C is present.
STEP 5: Now that you know it's a cos graph and you know what the period is, you're ready to sketch the graph.












The second graph we had to sketch was y=sin(x+π/4)



A useful Mnemonic would be DABC!

STEP 1: check if parameter D is present.
STEP 2: check if parameter A is present.
STEP 3: check if parameter B is present.
STEP 4: check if parameter C is present. Since C is the phase shift or horizontal shift and the value of C is +π/4, that means that the graph will shift to the left π/4 radians. It shifts to the left because in the original equation C is negative.
STEP 5: Now you're ready to sketch the graph. you know that it's a sin graph and it shifts horizontally to the left π/4 radians.













The next equation we had to graph was y=cos2(x-π/4).

STEP 1: check if parameter D is present.
STEP 2: check if parameter A is present.
STEP 3: check if parameter B is present. Since B is 2 that means that the period has changed. and to find the period you divide 2π/ B. So 2π/ 2 = π, the period is π. That means that there are now two waves between 0 and 2π.
STEP 4: check if parameter C is present.Since parameter C is the horizontal shift and the value of C is -π/4, that means the graph will shift to the right π/4 radians. It shifts to the right because in the original equation the value of C is negative.
It's like saying y=AcosB[x-(-C)]+ D. The negatives cancel.
STEP 5: Now that you know it's a cos graph and you know what the period and shift is, you're ready to sketch the graph.














We had to graph an equation with all the parameters, which was
y= -1/2sin3(x+π/6)+2.
REMEMBER: DABC!

STEP 1: D, the value of D is +2, so that means the sinusoidal axis is going to be shifted up +2. The sin graph will wind around this line.












STEP 2: check if parameter A is present. Since the value of parameter A < color="#000000">And since A
is negative that means it will be flipped. where the max's are they will now be min and where the min are they will be max's.












STEP 3: check if parameter B is present. Since B is 3 that means that the period has changed. and to find the period you divide 2π/ B. So 2π/ 3 = 2π/3, the period is 2π/3. That means that there are now three waves between 0 and 2π.












STEP 4: check if parameter C is present.Since parameter C is the horizontal shift and the value of C is π/6, that means the graph will shift to the right π/6 radians. It shifts to the right because in the original equation the value of C is negative.
It's like saying y=AcosB[x-(+C)]+ D. The value C stays negative.

STEP 5: Now that you know it's a cos graph and you know what the vertical shift, stretch, period, and what the phase shift is you're ready to sketch the graph.












Here's a link to see how the unit circle is related to the sin graph CLICK HERE!

And that summarizes today's math class.
Tomorrow, our scribe for the day will be
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ANTHONY

5 comments:

Mary Ann said...

well done samus! I like the diagrams. they were really easy to follow, along with your explanations. =D

LiON said...

whoaa..
i like the colours XD
and the graphs look pretty

Lani said...

Hi SAM,

Congratulations on writing a comprehensive, well illustrated scribe post! The clear labels on the graphs really added to clarity of your scribe.

Best wishes,
Lani

oliver_796 said...

Well done Samus! The graphs are awesome =).

SAMUS said...

thank you oliver,
thank you lani,
thank you lion,
thank you mary ann,
for the really nice comments :)