Note 2: Sine and Cosine Curve

1. 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

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°

3. 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 = 4sinx y = ⅔sinx

4. 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 = cos4x y = cos¼x

5. 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

6. 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

7. IN GENERAL: y = AsinBx + C To find: • Period = 360/B • Principal axis y = C Affects Amplitude Affects Period Affects Principal Axis

8. Examples: Sketch the following graphs: • y = 2sinx + 4 • y = -3sin2x • y = sin(0.5X) - 2 Write the equations for the following graphs:

9. Page 566 Exercise 18B.1