# f(t)=sin(2t)

f(t)=sin(2t)

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$f\left(t\right)=\mathrm{sin}\left(2t\right)$

Use the form $a\mathrm{sin}\left(bx-c\right)+d$ to find the variables used to find the amplitude, period, phase shift, and vertical shift.

$a=1$

$b=2$

$c=0$

$d=0$

Find the amplitude $|a|$.

Amplitude: $1$

Find the period of $\mathrm{sin}\left(2x\right)$.

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

$\frac{2\pi }{|b|}$

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

$\frac{2\pi }{|2|}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$.

$\frac{2\pi }{2}$

Cancel the common factor of $2$.

$\pi$

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$c$ and b$b$ in the equation for phase shift.

Phase Shift: $\frac{0}{2}$

Divide $0$ by $2$.

Phase Shift: $0$

List the properties of the trigonometric function.

Amplitude: $1$

Period: $\pi$

Phase Shift: None

Vertical Shift: None

Select a few points to graph.

$\begin{array}{cc}x& f\left(x\right)\\ 0& 0\\ \frac{\pi }{4}& 1\\ \frac{\pi }{2}& 0\\ \frac{3\pi }{4}& -1\\ \pi & 0\end{array}$

The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.