Question

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Question
Use the image to answer the question.

A waveform is drawn on a coordinate plane. The x-axis ranges from start fraction negative pi over 2 end fraction to 2 pi in increments of start fraction pi over 4 end fraction. The y-axis ranges from negative 3 to 3 in unit increments.
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Using the given graph, write an equation for a sine function.

(1 point)
y=

Remaining Attempts : 3

Answer 1

I can’t see the full graph clearly from the text alone. Could you either upload the picture or tell me 2–3 exact points on the graph (for example the x-values of a maximum and the next maximum, or a midline crossing with slope up and one maximum or minimum)? With that I’ll give the exact sine equation.

While you get that to me, here are the steps I’ll use so you know what I need and how the answer is formed:

1. Put the function in the standard form
y = A sin(B(x − C)) + D

2. Find A (amplitude) and D (vertical shift):
- A = (max − min) / 2
- D = (max + min) / 2

3. Find the period and B:
- period = distance between consecutive identical points (peak to peak, trough to trough, or midline-to-midline with same slope)
- B = 2π / period

4. Find phase shift C:
- For a sine, a convenient reference is a midline crossing with positive slope; C is the x-value of that crossing.
- If the graph’s sine starts at a maximum or other point, you can solve C from sin(B(x − C)) = value at a known x.

5. Determine sign (if graph is a reflected sine, you can write −A sin(…) instead).

If you give me the max and min x-values (or a midline crossing and a max), I’ll compute A, B, C, D and write the final equation.