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

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Presentation transcript:

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

Sin, Cos, Tan graph y=sin θ y=cos θ y=tan θ

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

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

Graph of secant y=sec θ Amplitude: Does not exist Period: 360° or 2π ←y=cos θ

Graph of cotangent y=cot θ Amplitude: does not exist Period: 180° or π ←y=tan θ

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:

Another example y=2 tan ½θ No amplitude Period:

Homework p even, 26, 28