How do you write equations in a single sine function?

Thread starter princiebebe57
Start date Feb 20, 2007
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Function Sine

In summary, to write an equation in a single sine function, you would use the formula y = A sin (Bx + C), where A represents the amplitude, B represents the frequency, and C represents the phase shift. The amplitude in a single sine function equation represents the maximum displacement of the graph from the horizontal axis and is half of the distance between the maximum and minimum values of the function. The frequency represents the number of cycles or repetitions of the function within a given unit of time and is inversely proportional to the period of the function. The phase shift represents the horizontal displacement of the graph from the origin and is determined by the value of C in the formula y = A sin (Bx + C). A positive value of

Feb 20, 2007

princiebebe57

What would the Domain, Range, Amplitude, Period, Phase shift be for y=-3sin(x)+2cos(x)?

How do you write it as a single sine function equivalent to it?

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Feb 20, 2007

JK423

Gold Member

When you have a function of
y=Asinωx+Bcosωx

that will be equivalent to:
y=Rcos(ωx+φ)

where R=sqrt(A^2+B^2) and φ=tan^-1 (A/B)

1. How do you write an equation in a single sine function?

To write an equation in a single sine function, you would use the formula y = A sin (Bx + C), where A represents the amplitude, B represents the frequency, and C represents the phase shift.

2. What does the amplitude represent in a single sine function equation?

The amplitude in a single sine function equation represents the maximum displacement of the graph from the horizontal axis. It is half of the distance between the maximum and minimum values of the function.

3. What is the frequency in a single sine function equation?

The frequency in a single sine function equation represents the number of cycles or repetitions of the function within a given unit of time. It is inversely proportional to the period of the function.

4. How do you determine the phase shift in a single sine function equation?

The phase shift in a single sine function equation represents the horizontal displacement of the graph from the origin. It is determined by the value of C in the formula y = A sin (Bx + C). A positive value of C would shift the graph to the right, while a negative value would shift it to the left.

5. Can a single sine function equation have a negative amplitude?

Yes, a single sine function equation can have a negative amplitude. This means that the graph would be reflected over the horizontal axis, with the maximum and minimum values interchanged. The negative amplitude would also affect the direction of the graph, making it decrease instead of increase as x increases.