find an equation of the form y = c+a sin(bx) with the max of 2,min of -2, and period of 3.
So far i've got 2sin___ . I don't know how to find the period.
Is it 2pi/3????
http://www.intmath.com/trigonometric-graphs/2-graphs-sine-cosine-period.php
To find the equation in the form y = c + a sin(bx) given the maximum, minimum, and period, we can use the properties of the sine function.
Let's start with the maximum and minimum values you mentioned. The maximum value of 2 and minimum value of -2 tell us that the amplitude, "a", of the sine function is 2. Amplitude is the distance from the average value of the function to its maximum or minimum value.
So now we have y = c + 2sin(bx). The equation is in the form we desire, with the amplitude defined.
Next, let's determine the period of the function. The period is the distance it takes for the function to complete one full cycle. In this case, the given period is 3.
The general formula to find the period of a sine function is given by 2π/b. Since we know the period is 3, we can set up the equation:
2π/b = 3.
To solve for b, we can rearrange the equation as:
b = 2π/3.
Now we have y = c + 2sin((2π/3)x). This equation satisfies the given conditions of having a maximum of 2, a minimum of -2, and a period of 3.
Keep in mind that the value of "c" is not specified in the given conditions. The value of "c" represents the vertical shift of the function, which would depend on any additional constraints or information you might have.