Final answer:
The value of cos(x) over the interval from 3π to 5 is −1.
This correct answer is b)
Step-by-step explanation:
Certainly! Let's break down the problem step by step:
Periodicity of the Cosine Function:
The cosine function has a period of 2π, which means it repeats its values every 2π radians.
In this problem, we are given the interval from 3×2π to 5×2π.
To simplify, let's convert this interval to a more standard form. Divide both endpoints by 2π to get the equivalent interval from 3 to 5.
Equivalent Interval:
The interval from 3 to 5 is effectively the same as the interval from −π to π.
Values of Cosine in the Interval from −π to π:
Evaluate the cosine function at key points in this interval.
cos(−π): The cosine of −π is −1.
cos(0): The cosine of 0 is 1.
cos(π): The cosine of π is −1.
Conclusion:
The values of the cosine function in the given interval are −1, 1 and −1.
Among the answer choices, the correct one is −1 (option b).
So, the detailed explanation confirms that the value of cos(x) over the interval from 3×2π to 5×2π is indeed −1.
This correct answer is b)