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

Thread starter ainster31
Start date Oct 17, 2013
Tags

Orthogonal Set

2 replies · 2K views · last reply Oct 17, 2013

ainster31

Thread starter
Oct 17, 2013

#1

Homework Statement

Textbook exercise text: Problems 7-12 ask to show the given sets of functions are orthogonal on the indicated interval and find each norm. Problem 7: {sin x, sin 3x, sin 5x, ...} on [0, pi/2]. Problem 8: {cos x, cos 3x, cos 5x, ...} on [0, pi/2]. Problem 9, highlighted: {sin nx}, n = 1, 2, 3, ... on [0, pi].

Homework Equations

The Attempt at a Solution

Handwritten-style math derivation: for m not equal to n, integral from 0 to pi of sin(mx)sin(nx) dx, rewritten as half the integral of cos(mx-nx) minus cos(mx+nx), evaluated to 1/2[sin(pi(m-n))/(m-n) - sin(pi(m+n))/(m+n)] = 0?

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

Discussion

arildno

Science Advisor

Homework Helper

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Dearly Missed

Oct 17, 2013

#2

What does sin(integer*pi) equal?

ainster31

Oct 17, 2013

#3

arildno said:

What does sin(integer*pi) equal?

It's equal to zero.

Wow. My trigonometry is terrible.

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