why is cos(-4x)=cos(4x)? teach me concepts. can add on to sin(-4x) tan(-4x)

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- Aug 23rd 2010, 07:41 AM #1

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- Aug 23rd 2010, 07:52 AM #2
Its because cos(x) is an

**even**function (symmetric about the y axis), meaning that . Now, sin(x) is an**odd**function (symmetric about the origin), meaning . You can see why this is the case by looking at the graphs of these two functions.

Now, tan(x) is an odd function, since .

Does this clarify things?

- Aug 23rd 2010, 09:04 AM #3

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- Aug 23rd 2010, 09:16 AM #4

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- Aug 23rd 2010, 10:24 AM #5

- Aug 23rd 2010, 11:28 AM #6

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- Aug 23rd 2010, 12:24 PM #7

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- Aug 23rd 2010, 12:33 PM #8

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If , then

hence, both angles have the same horizontal co-ordinate on the unit-circle.

Cos(angle)=horizontal co-ordinate of a point on the unit-circle circumference,

hence it can be located on the horizontal axis.

If

so the angles have the same horizontal co-ordinate.

Think of Cos(angle) as the horizontal co-ordinate of a point on the circle.

Sin(angle) is the vertical co-ordinate.

Tan(angle) is the slope of the line going through the origin (centre of unit-circle) and the point on the circle.

Or Tan(angle) is Sin(angle) divided by Cos(angle).

A positive angle is an anticlockwise movement starting at zero.

A negative angle is a clockwise movement starting at 360 degrees.