Find Amplitude, Period, and Phase Shift y=4/5sin(2pix)

$y = \frac{4}{5} \sin (2 π x)$

Step 1

Use the form $a \sin (b x - c) + d$ to find the variables used to find the amplitude, period, phase shift, and vertical shift.

$a = \frac{4}{5}$

$b = 2 π$

$c = 0$

$d = 0$

Step 2

Find the amplitude $| a |$ .

Amplitude: $\frac{4}{5}$

Step 3

Find the period of $\frac{4 \sin (2 π x)}{5}$ .

The period of the function can be calculated using $\frac{2 π}{| b |}$ .

$\frac{2 π}{| b |}$

Replace $b$ with $2 π$ in the formula for period.

$\frac{2 π}{| 2 π |}$

$2 π$ is approximately $6.2831853$ which is positive so remove the absolute value

$\frac{2 π}{2 π}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 π}{2 π}$

Rewrite the expression.

$\frac{π}{π}$

Cancel the common factor of $π$ .

Cancel the common factor.

$\frac{π}{π}$

Rewrite the expression.

$1$

Step 4

Find the phase shift using the formula $\frac{c}{b}$ .

The phase shift of the function can be calculated from $\frac{c}{b}$ .

Phase Shift: $\frac{c}{b}$

Replace the values of $c$ and $b$ in the equation for phase shift.

Phase Shift: $\frac{0}{2 π}$

Cancel the common factor of $0$ and $2$ .

Factor $2$ out of $0$ .

Phase Shift: $\frac{2 (0)}{2 π}$

Cancel the common factors.

Factor $2$ out of $2 π$ .

Phase Shift: $\frac{2 (0)}{2 (π)}$

Cancel the common factor.

Phase Shift: $\frac{2 \cdot 0}{2 π}$

Rewrite the expression.

Phase Shift: $\frac{0}{π}$

Divide $0$ by $π$ .

Phase Shift: $0$

Step 5

List the properties of the trigonometric function.

Amplitude: $\frac{4}{5}$

Period: $1$

Phase Shift: None

Vertical Shift: None

Step 6

Find Amplitude, Period, and Phase Shift y=4/5sin(2pix)

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