Algebra II

Part 1: Using complete sentences, compare the key features and graphs of sine and cosine. What are their similarities and differences?

Answer: The sine graph will always pass through (0, 0), While the cosine graph wouldn't. If the graph is 2cosx, it will pass through (0, 2). How high the graphs go depend on its amplitude, (how high or how far the graphs go can sometimes be infinite).

Part 2: Using these similarities and differences, how would you transform f(x) = 3 sin(4x - π) + 4 into a cosine function in the form f(x) = a cos(bx - c) + d?
Answer: I don't know, please help

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asked by Man
  1. trig identity:
    sin theta = cos (pi/2-theta)
    so
    y = 3 sin (4x-pi) + 4
    but from above trig identity
    y = 3 cos [ pi/2 - (4x-pi) ] + 4
    or
    y = 3 cos (-4x + 3 pi/2) + 4
    but
    cos (- theta) = cos theta
    so
    y = 3 cos (4x-3 pi/2) + 4

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    posted by Damon
  2. Thank you

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    posted by Man
  3. also in your explanation explain that the cosine curve is 90 degrees or pi/2 radians behind the sine curve if you graph y = sin theta and y = cos theta versus theta

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    posted by Damon
  4. You are welcome :)

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    posted by Damon
  5. By the way, there are an infinite number of solutions. eg 3 cos (4x - 7 pi/2)+4
    or
    - 3 cos(4x -pi/2) + 4
    etc

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    posted by Damon
  6. 3-x/(x+3)(x-3)

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    posted by debra
  7. is this right?

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    posted by Isabella
  8. this helped me a lot

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    posted by khloyie

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