Periodic functions and Trigonomotry unit test anyone? ALGEBRA 2 will offer cashapp in return for answers
What is the period of the function?
y=2 cos pi x
First question^
The period of the function is 2.
To determine the period of the function y=2cos(pi x), we need to understand the concept of a periodic function.
A periodic function is a function that repeats its values in a specific pattern over a particular interval or period. In the case of trigonometric functions, the period refers to the length of one complete cycle of the function.
In the given function, y=2cos(pi x), the coefficient of x inside the cosine function is pi. The coefficient of x affects the period of the function by changing the speed at which it repeats.
For a generic cosine function, y=a cos(bx), the period is given by the formula:
Period = 2π / |b|
In this case, b = π. Therefore, the period of the given function, y=2cos(pi x), is:
Period = 2π / |π|
Simplifying the expression:
Period = 2π / π
Period = 2
Thus, the period of the function y=2cos(pi x) is 2.