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Which of the following is not equivalent to cos pi over 5 1. Cos negative pi over 5 2. Cos 9pi over 5 3. Cos 4 pi over 5 4. Cos 11 pi over 5

User Zoonman
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2 Answers

2 votes
What is cos if u tell me i can answer

User Eric Wong
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5 votes

Answer:

The expression that is not equivalent to
\cos ((\pi)/(5)) is:

3.
\cos((4\pi)/(5))

Explanation:

We are asked to find which of the expression is not equivalent to:


\cos ((\pi)/(5))

1)


\cos((-\pi)/(5))

We know that:


\cos(-\theta)=\cos(\theta)

Hence, we get:


\cos((-\pi)/(5))=\cos((\pi)/(5))

Hence, option: 1 is incorrect.

2)


\cos((9\pi)/(5))

We know that:


\cos((9\pi)/(5))=\cos( 2\pi-(\pi)/(5))

As we know that:


\cos(2\pi-\theta)=\cos(\theta)

Hence, we have:


\cos((9\pi)/(5))=\cos((\pi)/(5))

Hence, option: 2 is incorrect.

4)


\cos((11\pi)/(5))

We know that:


\cos((11\pi)/(5))=\cos( 2\pi+(\pi)/(5))

As we know that:


\cos(2\pi+\theta)=\cos(\theta)

Hence, we have:


\cos((11\pi)/(5))=\cos((\pi)/(5))

Hence, option: 4 is incorrect.

3)


\cos((4\pi)/(5))

We know that:


\cos((4\pi)/(5))=\cos(\pi-(\pi)/(5))

As we know that:


\cos(\pi-\theta)=-\cos(\theta)

Hence, we have:


\cos((4\pi)/(5))=-\cos((\pi)/(5))\\eq \cos ((\pi)/(5))

Hence, option: 3 is the answer.

User Skatch
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6.9k points