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What is the value of cos(x) over the interval from 3 � 3π to 5 � 5π? a) 1 1 b) − 1 −1 c) 0 0 d) 1 2 2 1 ​

User Niyah
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1 Answer

3 votes

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)

User Ritesh Sinha
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