1. Graphing Trigonometric Functions Objectives: 1.Graph trig functions 2.Find the amplitude and period of variation of the sine, cosine and tangent functions

2. Sin, Cos, Tan graph y=sin θ y=cos θ y=tan θ -360-270-180 -9090180270360

3. Period and Amplitude Period – the distance the graph takes to finish a pattern before it begins to repeat itself. Amplitude – the absolute value of half the difference between its maximum value and its minimum value. For functions in the form y=a sin bθ, y= a cos bθ, and y=a tan bθ: Period - for sin and cos: or for tan: or Amplitude – for sin and cos:  a  for tan: not defined

4. Graph of cosecant y=csc θ Amplitude: Does not exist. Period: 360° ←y=sin θ 180 360 0 -180 -360

5. Graph of secant y=sec θ Amplitude: Does not exist Period: 360° or 2π -360-270-180 -9090180270360 ←y=cos θ

6. Graph of cotangent y=cot θ Amplitude: does not exist Period: 180° or π ←y=tan θ 180 360 0 -180 -360

7. Find the amplitude, if it exists and period of each function. Then graph y=sin ⅓ θ y=a sin bθ a=1, b= ⅓ Amp: 1period: Graph: 1080540270810

8. Another example y=2 tan ½θ No amplitude Period: 180 -180

9. Homework p. 767 16-22 even, 26, 28