How do you write equations in a single sine function?

Thread starter princiebebe57
Start date Feb 20, 2007
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Function Sine

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To convert the function y = -3sin(x) + 2cos(x) into a single sine function, it can be expressed as y = Rcos(ωx + φ), where R is calculated as R = sqrt((-3)^2 + (2)^2) and φ is determined using φ = tan^-1(-3/2). The domain of the function is all real numbers, while the range is from -R to R. The amplitude is the value of R, the period is 2π, and the phase shift is given by φ. This transformation simplifies the analysis of the function's properties.

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)

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