Amplitude and Period Calculator

"Amplitude and period Calculator"

This calculator determines the amplitude, length, phase shift, and vertical shift for a periodic sinusoidal function, including sine (f(x)=A⋅sin(Bx−C)+D) and cosine (f(x)=A⋅cos(Bx−C)+D).

Expertise the amplitude and duration is crucial because they assist to model a sinusoidal function’s styles over time.

The way to Calculate Amplitude and duration?

Methods to determine amplitude and length are as follows:

3.1. using Sine & Cosine phase Shift Equations:

Both its guide calculation or using amplitude and period calculator, those equations may be considered:

\(y = A \sin\left(Bx + C\right) + D\) or \(y = A \cos\left(Bx + C\right) + D\)

3.1.1. Amplitude:

\(\text{Amplitude} = A\)

3.1.2. Period:

\(B = \frac{2\pi}{|B|}\)

3.1.3. Phase Shift:

\(\text{Phase Difference} = -\dfrac{C}{B}\)

3.1.4. Vertical Shift:

\(\text{Vertical Shift} = D\)

3.2. Using Graph:

This technique works when you have the graph and may analyze it to determine values:

3.2.1. Amplitude:

1. Discover the imply line and height of the wave
2. Calculate the distance among these points
3. The recorded fee will be the amplitude

3.2.2. Period:

1. pick out two consecutive peaks of the wave
2. Calculate the horizontal distance between those two peaks
3. The end result might be the duration

Example:

The way to find amplitude and length for the following sinusoidal feature:

\(y = 4 \sin\left(3x - 2\right) + 6\)

Solution:

Step 1:

Find Amplitude

\(\text{Amplitude} = A\)

\(\text{Amplitude} = 4\)

Step 2:

Calculate the Period

\(\text{Period} = \frac{2\pi}{|B|}\)

\(\text{Period} = \frac{2\pi}{|3|}\)

\(\text{Period} = \frac{6.28}{3}\)

\(\text{Period} = 2.093\)

Step 3:

Find Phase Shift

\(\text{Phase Shift} = -\dfrac{C}{B}\)

\(\text{Phase Shift} = -\dfrac{-2}{3}\)

\(\text{Phase Shift} = \dfrac{2}{3}\)

\(\text{Phase Shift} = 0.667\)

Step 4:

Find Vertical Shift

\(\text{Vertical Shift} = D\)

\(\text{Vertical Shift} = 6\)

Associated Questions:

Is amplitude usually fine?

sure, because it defines the distance among imply and top points, that's continually superb. Our amplitude calculator can determine the amplitude of your sinusoidal function, considering each advantageous and poor values.

what is the amplitude of zero?

The amplitude of zero does no longer exist because the zero function represents a flat line that overlaps the equilibrium line. in this condition, the value of B becomes zero, which isn't a trigonometric feature.