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# Note 2: Sine and Cosine Curve PowerPoint PPT Presentation

Note 2: Sine and Cosine Curve. Draw an accurate sketch of the Sine and Cosine Curve: x -axis from 0° to 390° - plot every 15 ° y -axis from -1 to 1 – plot every 0.2. Characteristics of the Sine and Cosine Curve The period is 360 ° The amplitude is 1

Note 2: Sine and Cosine Curve

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### Note 2: Sine and Cosine Curve

Draw an accurate sketch of the Sine and Cosine Curve:

x-axis from 0° to 390° - plot every 15°

y-axis from -1 to 1 – plot every 0.2

Characteristics of the Sine and Cosine Curve

• The period is 360°

• The amplitude is 1

• The maximum value is 1 and minimum value is -1

• The domain is: 0° < x < 360°

• The range is: -1 < y < 1

• The cosine curve is just the sine curve shifted by 90°

Investigation 1:

Using technology plot the following:

y = sinx

y = 3sinx

y = 0.5sinx

For each graph:

• Find the maximum and minimum value

• Find the period and amplitude

Describe the effect of a in the function y = asinx

• What is the amplitude of:

y = 4sinxy = ⅔sinx

Investigation 2:

Using technology plot the following:

y = cosx

y = cos2x

y = cos(0.5x)

For each graph:

• Find the maximum and minimum value

• Find the period and amplitude

Describe the effect of b in the function y = cosbx

• What is the period of:

y = cos4xy = cos¼x

Investigation 3:

Using technology plot the following:

y = sinx

y = -sinx

y = -2sinx

Y = cosx

y = cos(-x)

y = cos(-3x)

For each graph:

• Find the maximum and minimum value

• Find the period and amplitude

Describe the effect of the negative in the trig functions

Investigation 4:

Using technology plot the following:

y = sinx + 2

y = sinx – 1

For each graph:

• Find the maximum and minimum value

• Find the period and amplitude

• Calculate the equation of the principal axis

What is the connection between:

y = sinx

y = sinx + c

IN GENERAL:

y = AsinBx + C

To find:

• Period = 360/B

• Principal axis y = C

Affects

Amplitude

Affects

Period

Affects

Principal Axis

Examples:

Sketch the following graphs:

• y = 2sinx + 4

• y = -3sin2x

• y = sin(0.5X) - 2

Write the equations for the following graphs:

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Exercise 18B.1