Is sin(nπ) always equal to zero for integer n?

Thread starter ainster31
Start date Oct 17, 2013
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Orthogonal Set

In summary, a set is orthogonal when all of its elements are mutually perpendicular to each other. To prove orthogonality, one must show that the dot product of any two elements is equal to zero. A set can be both orthogonal and linearly independent. Having an orthogonal set can make calculations easier and has practical applications in signal processing and data compression.

Oct 17, 2013

ainster31

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I'm not sure how to prove that it is zero. I don't see what I can do after the second last step.

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Oct 17, 2013

arildno

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What does sin(integer*pi) equal?

Oct 17, 2013

ainster31

arildno said:

What does sin(integer*pi) equal?

It's equal to zero.

Wow. My trigonometry is terrible.

1. What does it mean for a set to be orthogonal?

For a set to be orthogonal, it means that all of its elements are mutually perpendicular to each other. In other words, the dot product of any two elements in the set is equal to zero.

2. How do you prove that a set is orthogonal?

To prove that a set is orthogonal, you must show that the dot product of any two elements in the set is equal to zero. This can be done by finding the dot product algebraically or by showing that the angle between the elements is 90 degrees.

3. Can a set be both orthogonal and linearly independent?

Yes, a set can be both orthogonal and linearly independent. Orthogonality refers to the relationship between the elements, while linear independence refers to their individual linear combinations. A set can have both properties at the same time.

4. What are the benefits of having an orthogonal set?

Having an orthogonal set can make mathematical calculations easier and more efficient. This is because the dot product of any two elements in the set is equal to zero, which simplifies many equations. Additionally, orthogonal sets are often used in applications such as signal processing and data compression.

5. How does one use orthogonal sets in real-world applications?

Orthogonal sets have many practical applications, such as in signal processing and data compression. In signal processing, orthogonal sets can be used to efficiently represent and analyze signals. In data compression, they can be used to reduce the amount of data needed to represent a signal or image without losing important information.