the function y=cos(x) is dilated horizontally by a factor of 1/2 what's the new equation?
y=.......
and what is the period of the new function
y = cos(2x)
since 2x grows twice as fast as x, the graph is compressed into 1/2 the distance.
cos(kx) has a period of 2π/k
To horizontally dilate the function y = cos(x) by a factor of 1/2, we need to multiply the x-values by 2.
The new equation would be y = cos(2x).
The period of the new function can be found using the formula T = 2π / b, where b is the coefficient of x in the function.
In this case, b = 2, so the period of the new function is T = 2π / 2 = π.
To dilate a function horizontally by a factor of 1/2, you need to divide the variable inside the function by the dilation factor.
For the function y = cos(x), dividing x by 1/2 gives us y = cos(2x) as the new equation.
The period of the original cosine function is 2π, which represents one complete cycle. When you dilate the function horizontally by a factor of 1/2, the period of the new function changes.
To find the new period, divide the original period by the dilation factor, which is 1/2 in this case.
New period = Original period / Dilation factor
= 2π / 1/2
= 2π * 2
= 4π
Therefore, the new equation is y = cos(2x), and the new period of the function is 4π.