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

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Note 2: Sine and Cosine Curve

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Note 2 sine and cosine curve

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


Note 2 sine and cosine curve

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°


Note 2 sine and cosine curve

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


Note 2 sine and cosine curve

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


Note 2 sine and cosine curve

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


Note 2 sine and cosine curve

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


Note 2 sine and cosine curve

IN GENERAL:

y = AsinBx + C

To find:

  • Period = 360/B

  • Principal axis y = C

Affects

Amplitude

Affects

Period

Affects

Principal Axis


Note 2 sine and cosine curve

Examples:

Sketch the following graphs:

  • y = 2sinx + 4

  • y = -3sin2x

  • y = sin(0.5X) - 2

    Write the equations for the following graphs:


Note 2 sine and cosine curve

Page 566

Exercise 18B.1


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