what is the general equation of a sine function with an amplitude of 2, a period of $pi$ and a horizontal…

what is the general equation of a sine function with an amplitude of 2, a period of $pi$ and a horizontal shift of $pi$ units?\n$y = 2sin(2(x - pi))$\n$y = 2sin(4(x+pi))$\n$y=sin(0.5(x - pi))$\n$y=sin(2(x+pi))$

what is the general equation of a sine function with an amplitude of 2, a period of $pi$ and a horizontal shift of $pi$ units?\n$y = 2sin(2(x - pi))$\n$y = 2sin(4(x+pi))$\n$y=sin(0.5(x - pi))$\n$y=sin(2(x+pi))$

Answer

Answer:

A. $y = 2\sin(2(x - \pi))$

Explanation:

Step1: Recall sine - function general form

The general form of a sine function is $y = A\sin(B(x - C))+D$, where $A$ is the amplitude, $B$ is related to the period ($T=\frac{2\pi}{B}$), and $C$ is the horizontal shift.

Step2: Determine the amplitude $A$

Given that the amplitude $A = 2$.

Step3: Calculate the value of $B$

Since the period $T=\pi$ and $T=\frac{2\pi}{B}$, we substitute $T = \pi$ into the formula: $\pi=\frac{2\pi}{B}$. Solving for $B$ gives $B = 2$.

Step4: Determine the horizontal - shift $C$

Given that the horizontal shift is $\pi$ units, so $C=\pi$.

Step5: Write the function

Substituting $A = 2$, $B = 2$, and $C=\pi$ into $y = A\sin(B(x - C))$, we get $y = 2\sin(2(x - \pi))$.