Construct a sinusoid equation with the given amplitude and period that goes through the given point. (a.) Amplitude 3, period , point (0,0) (b.) Amplitude 1.5, period , point (5,0) State the amplitude and period of each equation, and (relative to the basic function) the phase shift and vertical translation. (a.)  (b.)

Expert Answers

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a.

A sinusoid that goes through (0,0) is a sine curve. Amplitude is 3. Assume period to be `2pi`

`y=3sinx`

b.

There is not enough information to complete this one. It could be a sine curve with a first x intercept (period/2) at (5,0).

`y=1.5sinbx`

The period would be:

`Period=(2pi)/b=10`

Then `b=pi/5`

The sinusoid equation would be `y=1.5sin(pi/5x)`

 

It could also be a cosine curve in which period/4=5. In this case

`Period=(2pi)/b=20`

And `b=pi/10`

Then the equation would be `y=1.5cos(pi/10x)`

 

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