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6-5 Translating Sine and Cosine

6-5 Translating Sine and Cosine. Phase Shift : A horizontal shift in trigonometric functions To phase shift, add/subtract c y= A sin (k θ + c) where the shift is Positive C- shift left Negative C- shift right.

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6-5 Translating Sine and Cosine

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  1. 6-5 Translating Sine and Cosine

  2. Phase Shift: A horizontal shift in trigonometric functions To phase shift, add/subtract c y= A sin (kθ + c) where the shift is Positive C- shift left Negative C- shift right

  3. (hint: when graphing with a phase shift, trying labeling in units same as phase shift)

  4. Describe the phase shift in y=sin(θ+π) • Describe the phase shift in y=cos(2θ - )

  5. Midline: a horizontal axis that is used as the reference line about which the graph of a periodic function oscillates (middle of the graph) Vertical Shift: add/subtract h to function such as: y= A sin(kθ + c) + h Positive h : shift up Negative h: shift down

  6. Lets Review y=A(sinkθ + C) + h Period (length) Amplitude (height) Vertical Shift (up/down) Phase Shift (left/right)

  7. 3) Given the function y=-2(cos4θ + ) -5, find the… • Amplitude • Period • Phase Shift • Vertical Shift • Midline equation

  8. 3) Given the function y=4 (cos2θ + ) +1, find the… • Amplitude • Period • Phase Shift • Vertical Shift • Midline equation

  9. Given the graph, fill in the blanks and write an equation to model the function: period _______ k=_______ maximum ______________ minimum ______________ amplitude ______________ vertical slide____________ phase shift (sine) _________c= sine equation ______________

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