Question

Write the equation of the trigonometric graph.5432|345.100waKOF100-1ين ته ان

Answer 1

Step 1: Write out the general sine function

$y=A\sin (B(x+C))+D$$\begin{gathered} \text{ Where} \\ A=\text{ the amplitude of the sine function} \\ \frac{2\pi}{B}=\text{ the period of the function} \\ C=\text{ the phase shift} \\ D=\text{ the vertical shift} \end{gathered}$

Step 2: Write out the values from the graph and substitute them into the general sine function

In this case,

$A=1$$\begin{gathered} \text{ the period is }\frac{\pi}{2} \\ \text{ therefore } \\ \frac{2\pi}{B}=\frac{\pi}{2} \\ \pi B=4\pi \\ \text{ thus} \\ B=4 \end{gathered}$

The period is π / 2. Therefore,

$\begin{gathered} BC=\frac{\pi}{2} \\ \text{ thus} \\ C=\frac{\pi}{2B}=\frac{\pi}{2\times4}=\frac{\pi}{8} \end{gathered}$

The vertical shift is downward by 2 units. Therefore,

$D=-2$

Hence, the equation of the trigonometric graph is given by

$\begin{gathered} y=\sin (4(x+\frac{\pi}{8}))-2 \\ \text{ thus} \\ y=\sin (4x+\frac{\pi}{2})-2 \end{gathered}$

y = sin (4x + p