# Solve the Sin Equation: Amp, Period, Phase Shift, Vert Shift

• datafiend
In summary, the amplitude of a sine wave is the distance from the midline to the highest or lowest point on the curve, the period is the length of one complete cycle and can be calculated by dividing 2π by the frequency or by using the unit circle, the phase shift is the horizontal displacement from the original position and the vertical shift is the vertical displacement from the equilibrium position. To solve a sin equation, use the general form and plug in the given values for amplitude, period, phase shift, and vertical shift to find the solutions.
datafiend

## Homework Statement

Find the amplitude, period, phase shift, and vertical shift

## Homework Equations

y=- $1/2$sin [3 (x-∏/2)] -2

## The Attempt at a Solution

amp = -$1/2$, vertical shift is 2 down y-axis.

I can't get the period and ph. shift.

The "standard" sine function, sin(x), has one period starting at $x= 0$ and ending at $x= 2\pi$. The function sin(a(x- b)) has one period starting at $a(x- b)= 0$, or $x= b$ and ending at $a(x- b)= 2\pi$ or $x= b+ \frac{2\pi}{a}$.

1 person

## 1. What is the amplitude of a sine wave?

The amplitude of a sine wave is the distance from the midline to the highest or lowest point on the curve. It represents the maximum displacement of the wave from its equilibrium position.

## 2. How is the period of a sine wave calculated?

The period of a sine wave is the length of one complete cycle of the wave. It can be calculated by dividing 2π by the frequency of the wave, or by dividing the circumference of the unit circle by the x-coordinate of a point on the wave.

## 3. What is the phase shift of a sine wave?

The phase shift of a sine wave is the horizontal displacement of the wave from its original position. It is usually measured in radians or degrees and can be positive or negative depending on the direction of the shift.

## 4. How does the vertical shift affect a sine wave?

The vertical shift of a sine wave is the vertical displacement of the wave from its equilibrium position. It is usually measured in units or degrees and can be positive or negative depending on the direction of the shift. The vertical shift does not affect the shape or period of the wave, but only its position on the y-axis.

## 5. How do I solve a sin equation with given values for amplitude, period, phase shift, and vertical shift?

To solve a sin equation, you can use the general form of the equation: y = A*sin(Bx+C) + D, where A is the amplitude, B is the frequency (1/period), C is the phase shift, and D is the vertical shift. Plug in the given values and solve for x to find the solutions to the equation.

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