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Note 2: Sine and Cosine Curve

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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