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

Results 1 to 8 of 8

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

- Joined
- Aug 2010
- From
- Singapore
- Posts
- 93

- August 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?

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

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 11,751
- Thanks
- 652

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

- Joined
- Aug 2010
- From
- Singapore
- Posts
- 93

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

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

- Joined
- Aug 2010
- From
- Singapore
- Posts
- 93

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

- Joined
- Mar 2010
- Posts
- 715
- Thanks
- 2

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

- Joined
- Dec 2009
- Posts
- 3,120
- Thanks
- 1

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.