Question

What is the period of the graph of y = 2 cos (π/3 x) + 3?

A) 2
B) 3/π
C) 6
D) π/3

Answer 1

The period of the graph of the given function y = 2 cos (\(π/3\) x) + 3 can be calculated as 2\(π\) divided by (\(π/3\)), which simplifies to 6. This is option C).

Step-by-step explanation:

The question is asking to find the period of the graph of the function y = 2 cos (\(\pi/3\) x) + 3.

To find the period of a cosine function of the form y = A cos(Bx) + C, where A, B, and C are constants, the general period of the function is given by 2\(\pi\)/B. In this case, the value of B is \(\pi/3\), so the period of the graph would be 2\(\pi\) divided by \(\pi/3\).

Calculating the period:

1. Divide 2\(\pi\) by \(\pi/3\).
2. Multiply by the reciprocal of \(\pi/3\), which is 3/\(\pi\).
3. So, 2\(\pi\) * 3/\(\pi\) = 6

Therefore, the period of the graph is 6, which matches option C).