what is the period of y= sin 6(x) and y= cos (-1/3)x
To find the period of a trigonometric function, you need to determine the horizontal length of one complete cycle of the graph.
For the function y = sin(6x), the coefficient of x inside the sine function is 6. The general formula to find the period is given by:
Period = (2π) / |coefficient of x|
Therefore, for y = sin(6x), the period can be calculated as:
Period = (2π) / 6 = π/3
So, the period of y = sin(6x) is π/3.
Similarly, for y = cos((-1/3)x), the coefficient of x inside the cosine function is -1/3. Applying the same formula:
Period = (2π) / |coefficient of x|
Period = (2π) / (1/3) = 6π
So, the period of y = cos((-1/3)x) is 6π.