# 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 Fl4shI 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.

Thanks alot.

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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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Does a right triangle always equal 180 degrees?

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The internal angles of all triangles add up to 180.

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Quote:
 Original post by CDPropThe internal angles of all triangles add up to 180.

Not on the surface of a sphere :)

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