Question

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

Answer 1

What is cos if u tell me i can answer

Answer 2

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.