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Fl4sh

How do you visualize the relationships between sin,cos,tan

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I understand the basics and I understand that they are just functions that take an angle and return a ratio of the two sides of a right triangle.

My question is how do I visualize this stuff?

And also, how come you can multiply a distance by what one of the functions return and have it give a side? ;o

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Quote:
Original post by Fl4sh
I understand the basics and I understand that they are just functions that take an angle and return a ratio of the two sides of a right triangle.

My question is how do I visualize this stuff?

And also, how come you can multiply a distance by what one of the functions return and have it give a side? ;o


Ugly ascii art time:



/
1 / |
/ | sin(v)
/ |
/ ) v |
--------------
cos(v)

Look at the unit circle


1) sin(v) and cos(v) can be defined defined as the sides of the triangle you get by drawing a v angle line from origin inside a 1 radius circle

2) increasing the radius of the circle increases the length of the sides of the triangle by the same factor.

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My visualizations:

cos is the X coordinate as you rotate around a circle. Changes slowest toward the left and right (0 and 180 degrees), fastest at the top and bottom (90 and 270 degrees).

sin is the Y coordinate. Changes fastest at top and bottom, slowest at left and right.

tan is the slope of the line. 0 at left and right, ramps faster and faster to infinity at the top and bottom.

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