Understanding Trigonometric Functions and Their Geometric Meaning

[ViolentCorpse]

I'm not sure if this is the correct section for this thread since this isn't homework, but my question is very basic, so I think this section is suitable.

I have two questions regarding the trigonometric functions (sinx,cosx,tanx etc).

1) What is the geometric meaning (i.e in the context of a right-angle triangle) of functions like cos(180°) or any of the trigonometric functions with an obtuse angle? I mean a right-angle triangle can not contain an obtuse angle so I don't understand how we can have ratios of two sides of a right-triangle that isn't even a right-triangle to begin with (if that makes any sense)?

2) Why are these functions negative for some angles? Since these are just ratios of any two lengths of a right-triangle and lengths usually aren't negative.

Pardon my ignorance and thank you for your precious time! :)

 

[Mark44]

I'm not sure if this is the correct section for this thread since this isn't homework, but my question is very basic, so I think this section is suitable.

I have two questions regarding the trigonometric functions (sinx,cosx,tanx etc).

1) What is the geometric meaning (i.e in the context of a right-angle triangle) of functions like cos(180°) or any of the trigonometric functions with an obtuse angle? I mean a right-angle triangle can not contain an obtuse angle so I don't understand how we can have ratios of two sides of a right-triangle that isn't even a right-triangle to begin with (if that makes any sense)?

2) Why are these functions negative for some angles? Since these are just ratios of any two lengths of a right-triangle and lengths usually aren't negative.

Pardon my ignorance and thank you for your precious time! :)

The trig functions are not limited to angles in right triangles. They are defined in terms of the coordinates of points on the unit circle. The angle is the one between two rays: the ray from (0, 0) to (1, 0), and another ray from the origin to an arbitrary point on the unit circle. The x-coordinate of this point is the cosine of the angle, and the y-coordinate of this point is the sine of the angle. See http://en.wikipedia.org/wiki/Unit_circle.

 

[ViolentCorpse]

Oh. That was very helpful. Thanks a lot, Mark44! :)