# Problem understanding negative angles...

1. Dec 8, 2015

### Dave Ritche

I'm having problem understanding why negative angle of cosine is a positive value but negative of sine is a negative sine angle?why is this so?can someone please help me with this confusion?

COS(-angle)=COS(angle)
Sin(-angle)=-Sine(Angle)

2. Dec 8, 2015

3. Dec 8, 2015

### Dave Ritche

Thanks but if I was able to understand from Wikipedia then I would not have been on the PF.

4. Dec 8, 2015

### Staff: Mentor

Do you understand the basic idea of the trigonometric circle? That the cosine of the angle is given by the projection on the x axis, and the sine by the projection on the y axis? Then you should see why the relation for negative angles. Since 0 (degrees or radians) is along the x axis, both α and -α have the same projection on x, while they lead to equal both opposite projections on y.

5. Dec 8, 2015

### Dave Ritche

No,do
Can't understand that..really baffled. .

6. Dec 8, 2015

7. Dec 8, 2015

### jbriggs444

Imagine something one mile in front of you and slightly downhill. The angle to this object, compared to the horizontal is negative. But the object is still one mile in front of you. The fact that it is downhill does not mean that it is behind you.

8. Dec 8, 2015

### Staff: Mentor

°
It's not true in general that the cosine of a negative angle is positive, or that the sine of a negative angle is negative. It depends on the quadrant of the unit circle that the angle is in.

For example, $\cos(-120°) = -1/2$ and $\sin(-210°) = + 1/2$.

9. Dec 8, 2015

### ElijahRockers

Perhaps a better way to tackle this issue would be to discuss the meaning of even and odd functions.

Keep in mind here sine is an odd function, and cosine is an even function. But this definition of even and odd functions applies to many different functions, not just sine and cosine.

I get the feeling that OP is actually wondering about this property of even and odd functions, but has just worded his question ambiguously.

10. Dec 11, 2015