Sine Function
Directions: Graph the sine curve. Use all angles in the unit circle starting with 0 and ending with 360. Each ordered pair will be (angle, sine value).
Example: the sin0=0, so the ordered pair is (0,0)
GENERAL FORM: f(x)=Asin(Bx+C)+D
Directions: Open the “Sine and Cosine” Sketchpad. On the sine page, move the values to the indicated values and sketch the graphs. Then determine what each variable does to the curve.
1. A=2, B=1, C=0, D=0 2. A= -½ , B=1, C=0, D=0
3. A=1, B=2, C=0, D=0 4. A=1 , B=½ , C=0, D=0
5. A=1, B=1, C=∏, D=0 6. A= 1 , B=1, C= -∏/2, D=0
approximate pi as a decimal approximate pi as a decimal
7. A=1, B=1, C=0, D=1 8. A= 1 , B=1, C= 0, D= - ½
approximate pi as a decimal approximate pi as a decimal
f(x)=Asin(Bx+C)+D / Transformation/Impact: / How to determine it:
Examples: Determine all variables/transformations and then graph the curve.
1. y=2sin(x+π)
Amplitude=
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2. y= sin(2x)+1
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3. y=sin(3x-135)
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Cosine Function
Directions: Graph the cosine curve. Use all angles in the unit circle starting with 0 and ending with 360. Each ordered pair will be (angle, sine value).
Example: the cos0=1, so the ordered pair is (0,1)
GENERAL FORM: f(x)=Acos(Bx+C)+D
Directions: Open the “Sine and Cosine” Sketchpad. One the cosine page, move the values to the indicated values and sketch the graphs. Then determine what each variable does to the curve.
1. A=1.5, B=1, C=0, D=0 2. A= -1, B=1, C=0, D=0
3. A=1, B=4, C=0, D=0 4. A=1 , B=½ , C=0, D=0
5. A=1, B=1, C=∏/2, D=0 6. A= 1 , B=1, C= -∏/4, D=0
approximate pi as a decimal approximate pi as a decimal
7. A=1, B=1, C=0, D=1 8. A= 1 , B=1, C= 0, D= - ½
approximate pi as a decimal approximate pi as a decimal
f(x)=Acos(Bx+C)+D / Transformation/Impact: / How to determine it:
Examples: Determine all variables/transformations and then graph the curve.
1. y=2cosx-1
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2. y= cos(3x)-1
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3. y=cos( ½x+π/4)
Amplitude=
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