Question

Find the period of the function. y = 5 cos (1/2)x
a) 4π
b) 5
c) π/2
d) 5π/2

Answer 1

The period of the cosine function y = 5 cos (1/2)x is found using the formula T = 2π / |B|, with B being the coefficient of x. Here B equals 1/2, resulting in a period of 4π.

Step-by-step explanation:

To find the period of the function y = 5 cos (1/2)x, we need to recall the general form of a cosine function which is y = A cos(Bx - C) + D, where:

• A is the amplitude,
• B affects the period,
• C is the phase shift,
• and D is the vertical shift.

In the given function, B = 1/2. The period of a cosine function is found using the formula T = 2π / |B|. Thus, the period of the given function is:

T = 2π / |1/2|

= 2π / 0.5

= 4π

So, the correct answer is (a) 4π.