What is the period of the function f(x)=-6sin(3pix+4)-2?
The period of the function f(x)=-6sin(3pix+4)-2 is 2π/3.
To find the period of the function f(x) = -6sin(3πx+4)-2, we need to consider the coefficient of x inside the sine function.
In this case, the coefficient of x is 3π.
The period of a sine function is given by 2π divided by the coefficient of x. So, the period of f(x) is:
Period = 2π / (3π) = 2/3
Therefore, the period of the function f(x) = -6sin(3πx+4)-2 is 2/3.
To find the period of a function of the form f(x) = a sin(bx + c) + d, where a, b, c, and d are constants, we can use the formula: Period = 2π/|b|.
In this case, for the function f(x) = -6sin(3πx + 4) - 2, we can see that b is equal to 3π. Therefore, to find the period, we can use the formula:
Period = 2π/|3π|
Since |3π| = 3π, we can simplify the expression to:
Period = 2π/3π
Simplifying further, we have:
Period = 2/3
So, the period of the function f(x) = -6sin(3πx + 4) - 2 is 2/3.