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Warm UP

Warm UP. 1) Name the following parent graph: 2) Where is the period for the function y=cot(x)? 3) What is the point of inflection for y=sin(x)?. General Trig Function Equation. Amplitude (A) – makes the graph shorter or taller; vertical stretch

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Warm UP

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  1. Warm UP 1) Name the following parent graph: 2) Where is the period for the function y=cot(x)? 3) What is the point of inflection for y=sin(x)?

  2. General Trig Function Equation • Amplitude (A) – makes the graph shorter or taller; vertical stretch • Period (B) – how fast the wave is going; horizontal stretch • Phase Shift (H)– horizontal shift; left or right (opposite!) • Phase Displacement (K)– vertical shift; up or down (same!)

  3. Period • Period =

  4. Example 1 • Let y = 4 sin x. What transformation of the parent sine function is this? • How would the transformed graph compare to the graph of the parent function? • Check your guess by graphing both the parent sinusoid and the transformed sinusoid on the same screen.

  5. Describe the transformations of the parent function: • y = 2 sin (x – 45) • y = cos(2x – 180) + 1 • y = tan (x + 90) – 2

  6. Graphing Example 1 Graph one period of f(x) = 2cos (3x + 45o)-1 Amplitude: _______ Period: _______ Phase shift: _______ Vertical Shift: _______

  7. Transformation Example 2 Graph one period of f(x) = 5tan(.5x - 45) – 1 Amplitude: _______ Period: _______ Phase shift: _______ Vertical Shift: _______

  8. Transformation Example 3 Graph one period of f(x) = sin (2x + 180) + 3 starting with the phase shift. Amplitude: _______ Period: _______ Phase shift: _______ Vertical Shift: _______

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