I learned in my geometry class that sine, cosine, and tangent were triangle angle ratios. Exactly how do sin, cos, and tan effect superscopes and movements. I heard something about triangle angle ratios being in degress and superscopes and movements being in rads, but I don't know what that means. Can somebody please explain this to me?
Announcement
Collapse
No announcement yet.
Sin, Cos, Tan
Collapse
X

Trigonometry
The easiest way to explain is this:
Given a circle with radius 1 (the so called 'unitcircle'). We take a random point on this circle. We can describe this point uniquely by the angle of the radius through this point and the Xaxis, for example 90°, 140°, ...
Mathematically however, radians are used instead of degrees. Without going into much theory, you should just remember that 360° = 2*PI.
So suppose we have a point lying at N radians on our unit circle. Then the X coordinate will be given by cos(N), and the Y coordinate by sin(N). That's the definition of cosine and sine.
So if you want to draw a circle, take every value A from 0 to 2*PI, and plot the points (cos(A), sin(A)). Easy.
The relationship of sine and cosing with rightangled triangles is pretty easy to see. Draw a circle using the origin (0,0) as center. Take a point on this circle, connect the point with the center, project the point on the X axis. Voilà: a rightangled triangle appears
Sin and cos have other uses as well. Because they are coordinates of points lying on a circle, they are periodic. A point traveling along a circle will eventually arrive at its starting point. This means that their values are repetive after a while (2*PI to be exact).
So you can use sine and cosine as a source for a pulsing/wavy scope or movement.
The tangent tan is defined as sin divided by cos. It ranges from negative infinity to positive infinity in PI/2 to PI/2, and repeates itself every PI.
Usually you won't need the actual mathematical uses of these functions, but you'll rather be using their characteristics (e.g. repetiveness).
Comment

Comment