Find the period of the function y = -5 cos (x). A) 5 B) 𝜋5 C) 2⋅𝜋 D) 𝜋

Answer 1

The standard form of a cosine function is y = A cos(Bx + C), where B is the coefficient of x.

The frequency f is defined as the number of cycles that occur in one unit of the independent variable. 

The absolute value of A represents the amplitude. The absolute value of B will help us determine the frequency or the period (reciprocal of the frequency) and C represents the phase shift. 

In the case of the cosine function, one cycle is completed when the argument Bx + C increases by 2𝜋, where we go through the whole circle, at which point the cosine has its maximum value 1.

Amplitude is |A| = 5 and coefficient |B| = 1 = B and C = 0

The period represents the length of one complete cycle of the function. The period T is once again the reciprocal of the frequency.

The formula for the period T is the following:

T= 2π / |B|

Since B=1 above, T = 2π

The correct answer is C.

It would be useful to know the following:

The period represents the length of one complete cycle of the cosine function. It is the distance between two consecutive peaks or troughs of the function. The period is calculated by dividing 2π by the absolute value of the coefficient B.

The amplitude A affects the vertical scale of the cosine function, representing the maximum value of the function. The phase shift c determines the horizontal shift of the function.

Answer 2

The period is 2π divided by the coefficient on the variable.