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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. Describe the phase shift in y=sin( θ + π )

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

  4. 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

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

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

  7. To Graph by hand… • Find the vertical shift, and graph the midline. • Find the amplitude. Sketch out highest/lowest point • Find the period, then graph the sin/cos function • Shift the function over for the appropriate phase shift

  8. 4) Find the amplitude, period, phase shift, and midline of the function, then graph y= 4(cos+π) -6

  9. Find the amplitude, period, phase shift, and midline of the function, then graph y=-2(cos𝜃/3+4π) +1

  10. Compound Function: a graph that consists of sums or products of both trigonometric and linear functions Ex) y= sinx * cosx y= x + sinx To graph: Graph both functions on the same axis. Then, add/multiply the corresponding coordinates to find the new y value.

  11. Graph y = x + cosx

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