Wednesday, February 28, 2018

Patterns even emerge from the equations for these things...........


Unit Circle

unit circle center at (0,0)

The "Unit Circle" is a circle with a radius of 1.
Being so simple, it is a great way to learn and talk about lengths and angles.
The center is put on a graph where the x axis and y axis cross, so we get this neat arrangement here.

unit circle center at (0,0)

Sine, Cosine and Tangent

Because the radius is 1, we can directly measure sine, cosine and tangent.
unit circle center angle 0
What happens when the angle, θ, is 0°?
cos 0° = 1, sin 0° = 0 and tan 0° = 0
unit circle center angle 90
What happens when θ is 90°?
cos 90° = 0, sin 90° = 1 and tan 90° is undefined

Try It Yourself!

Have a try! Move the mouse around to see how different angles (in radians or degrees) affect sine, cosine and tangent

The "sides" can be positive or negative according to the rules of Cartesian coordinates. This makes the sine, cosine and tangent change between positive and negative values also.

No comments:

Post a Comment