graphing sin & cos

​-We just learned why y=sinx looks like this.

-Now we see what happens when we put an "a" in front and see what happens when we graph y=asinx

• ​The amplitude is half the distance from the max to the min

• ​Think of it as how far the max is from the "midline"

• ​Amplitude is always positive, thus amplitude = |a|

• ​The red graph has an amplitude of 1

• ​The blue graph has an amplitude of 2

• ​What happens if we add/subtract a number?

• ​The k is the "midline"

• ​Where can we draw the midline, this is our k

• ​k shifts the graph up (+k) and down (-k)

• ​What is the a?

• ​What is the k?

• ​What does the h do?

• ​The red graph is y=sinx

• ​The blue graph is

• ​If h is positive then it shifts right example: y=sin(x-pi)

• ​If h is negative then it shifts left

  example: y=sin(x+pi)

• ​The key is to highlight one "S" in the sin curve, when you have the starting point, that gives you the h

• ​There are multiple options!!!

• ​What happens when we change the b?

• ​The blue graph is y = sin x

• ​The red graph is y = sin bx

• ​Look for one cycle of sin, this is called the "period"

• ​Bigger b's give smaller periods

• ​Smaller b's give bigger periods

• ​Now that we can find the period. we can calculate the b

• ​period = pi

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• ​so b = 2

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• ​y = sin b(x-h) or y = a sin (bx-c)

• If we get y = sin b(x-h) we can instantly determine the period and shift

• ​If you get y = sin (bx-c), we can instantly determine the period BUT we have to factor out the b to get y=sinb(x-h) in order to see the shift!