Explain how do you find the period of Y = cos(6x) from your graph. what is the period of Y= cos(6x) in radians?
when 6 x = 2 pi, that is a period
change in x = pi/3 is once around
To find the period of the function Y = cos(6x) from the graph, we need to understand the concept of the period. The period refers to the length of one complete cycle of the function. In trigonometric functions like cos(6x), the period is typically determined by dividing 2π (in radians) by the coefficient of x within the parentheses.
For the given function Y = cos(6x), the coefficient of x is 6. So, we can find the period using the formula:
Period = 2π / coefficient of x
In this case, the coefficient of x is 6. Therefore, the period would be:
Period = 2π / 6
Simplifying further, we get:
Period = π / 3
Hence, the period of Y = cos(6x) in radians is π/3.
To find the period of the function Y = cos(6x) from the graph, you need to identify the distance between successive peaks or troughs of the cosine curve. The period of a function is the horizontal distance it takes for the function to repeat its pattern.
First, let's understand the general form of a cosine function: Y = cos(kx), where k represents the coefficient of x. In this case, the coefficient is 6.
For the function Y = cos(6x), the coefficient 6 indicates that the argument of the cosine function, 6x, goes through a full cycle within a certain distance. To find the period, we need to determine the distance required for 6x to go from 0 to 2π (or any other multiple of 2π).
In radians, a full cycle of the cosine function is represented by 2π. Since the coefficient of x is 6 in our function (Y = cos(6x)), it means that the argument of the cosine function, 6x, goes through one full cycle within 2π units.
To find the period of the function Y = cos(6x) in radians, we divide the period of a general cosine function (2π) by the coefficient of x.
Therefore, the period of Y = cos(6x) in radians is 2π/6, which simplifies to π/3.