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Which expression will give you the phase shift when the standard form is f left parenthesis x right parenthesis equals a sine left parenthesis b x plus c right parenthesis plus d?

Sagot :

MrRoyalidn

Answer:

[tex]Phase\ Shift = -\frac{c}{b}[/tex]

Step-by-step explanation:

See comment for complete question

Given

[tex]f(x) = Asin(bx+c)+d[/tex]

Required

Determine an expression for the phase shift

[tex]f(x) = Asin(bx+c)+d[/tex]

Factorize the expression in bracket

[tex]f(x) = Asin(b(x+\frac{c}{b}))+d[/tex]

The general expression is:

[tex]F(t) = A f(B(t - C/B)) + D[/tex]

Where:

C/B is the phase shift

By comparing the general expression with: [tex]f(x) = Asin(b(x+\frac{c}{b}))+d[/tex]

[tex]-\frac{C}{B} = \frac{c}{b}[/tex]

Multiply both sides by -1

[tex]\frac{C}{B} = -\frac{c}{b}[/tex]

Hence:

[tex]Phase\ Shift = -\frac{c}{b}[/tex]

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