- #1

physics=world

- 110

- 0

**1. (sin4x + cos4x)**

## Homework Equations

## The Attempt at a Solution

(sin4x + cos4x)

= (sin4(-x) + cos4(-x))

= -sin4x + cos4x

im thinking it is an even function

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- Thread starter physics=world
- Start date

- #1

physics=world

- 110

- 0

(sin4x + cos4x)

= (sin4(-x) + cos4(-x))

= -sin4x + cos4x

im thinking it is an even function

- #2

slider142

- 1,015

- 70

- #3

Mark44

Mentor

- 36,310

- 8,281

You started off by saying sin(4x) + cos(4x) = sin(-4x) + cos(-4x), which your later work shows isn't true. Your work should start with sin(-4x) + cos(-4x). If you can show this is equal to sin(4x) + cos(4x), then the function is even. If it turns out to be equal to -sin(4x) - cos(4x), then the function is odd. If it results in neither, then the function is neither even nor odd.1. (sin4x + cos4x)

## Homework Equations

## The Attempt at a Solution

(sin4x + cos4x)

= (sin4(-x) + cos4(-x))

= -sin4x + cos4x

im thinking it is an even function

- #4

physics=world

- 110

- 0

so is it an odd function since it does not look like the original function?

- #5

Michael Redei

- 181

- 0

- #6

slider142

- 1,015

- 70

so is it an odd function since it does not look like the original function?

A function is odd if it has a

A quick way to compare two expressions is to subtract one from the other. It doesn't matter which one comes first, as if they are the same value, the subtraction will give you 0. If you don't get 0, the expressions are different.

If your function is not odd, that does not mean it is even. To be even it must satisfy a different

Most functions are neither even nor odd.

Last edited:

- #7

HallsofIvy

Science Advisor

Homework Helper

- 43,021

- 970

You appear to thinking that any function that is not "even" must be "odd". That is not true. slider142, in the first response to your post, told you that a function is odd if and only if f(-x)= -f(x). slider142 also told you that "most functions are neither even nor odd."so is it an odd function since it does not look like the original function?

- #8

Michael Redei

- 181

- 0

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