Answered

Get the information you need with the help of IDNLearn.com's expert community. Find the information you need quickly and easily with our comprehensive and accurate Q&A platform.

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]

We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.