Find Amplitude, Period, and Phase Shift v(t)=0.5sin(970pit)

$v (t) = 0.5 \sin (970 π t)$

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

$a = 0.5$

$b = 970 π$

$c = 0$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $0.5$

Find the period of $0.5 \sin (970 π t)$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $970 π$ in the formula for period.

$\frac{2 π}{| 970 π |}$

$970 π$ is approximately $3047.34487398$ which is positive so remove the absolute value

$\frac{2 π}{970 π}$

Cancel the common factor of $2$ and $970$ .

Factor $2$ out of $2 π$ .

$\frac{2 (π)}{970 π}$

Cancel the common factors.

Factor $2$ out of $970 π$ .

$\frac{2 (π)}{2 (485 π)}$

Cancel the common factor.

$\frac{2 π}{2 (485 π)}$

Rewrite the expression.

$\frac{π}{485 π}$

Cancel the common factor of $π$ .

Cancel the common factor.

$\frac{π}{485 π}$

Rewrite the expression.

$\frac{1}{485}$

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: $\frac{0}{970 π}$

Cancel the common factor of $0$ and $970$ .

Factor $970$ out of $0$ .

Phase Shift: $\frac{970 (0)}{970 π}$

Cancel the common factors.

Factor $970$ out of $970 π$ .

Phase Shift: $\frac{970 (0)}{970 (π)}$

Cancel the common factor.

Phase Shift: $\frac{970 \cdot 0}{970 π}$

Rewrite the expression.

Phase Shift: $\frac{0}{π}$

Divide $0$ by $π$ .

Phase Shift: $0$

List the properties of the trigonometric function.

Amplitude: $0.5$

Period: $\frac{1}{485}$

Phase Shift: None

Vertical Shift: None

Find Amplitude, Period, and Phase Shift v(t)=0.5sin(970pit)

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