Question

How can I create a sine graph that has a period of 2π and an amplitude of 3?

Answer 1

Hello!

The parent function of the graph of sin is y = sin(x).

Amplitude is the maximum displacement on the graph of a function.

Period is the displacement of x at which the graph of a function begins to repeat.

The period can be found by using the formula: $P = \frac{2\pi}{B}$.

Since the amplitude is 3, the graph of sin is y = 3sin(x).

Given the period 2π, we can substitute this value into the given formula, $P = \frac{2\pi}{B}$, to find B.

2π = 2π / B (multiply B to both sides)

2π · B = 2π (divide by 2π)

B = 1

Thus, the equation is y = 3sin(x). I'll post the graph as well.