A little confused on this one...
Find the amplitude and the period of h(x) = 1/2 cos (-πx).
as usual,
amplitude = 1/2
period = 2π/π = 2
The - sign doesn't mean anything here, since cos(-x) = cos(x)
I was thinking that was the answer, but I just wasn't sure if those pi's were going to cancel out. Thanks for the confirmation! :)
To find the amplitude and the period of the function h(x) = 1/2 cos (-πx), let's break it down step by step.
First, let's look at the general form of a cosine function: y = A cos(Bx + C) + D, where A is the amplitude, B determines the period, C is the phase shift, and D is the vertical shift.
In our case, h(x) = 1/2 cos (-πx). Notice that the coefficient of x inside the cosine function is -π. This means that B = -π.
Now, let's find the amplitude. The amplitude (A) is the maximum absolute value of the function. Since the coefficient of cos is 1/2, we can say that A = 1/2.
Next, let's determine the period. The period (P) of a cosine function is given by P = 2π/|B|. In our case, B is -π, so the period is P = 2π/|-π| = 2π/π = 2.
Therefore, the amplitude of h(x) is 1/2 and the period is 2.