You should also notice in the figure that tangent equals sine(θ) over cosine(θ). You may also remember that sine and cosine are similar when you graph them, both forming periodic waves. Only the cosine wave is shifted a bit (90° or pi/2) on the graph, which is technically called a phase shift. I fully realize that it is a difficult to deal with this stuff in the abstract. Fortunately, there is another model, the unit circle (shown below) used to visualize and study the trig functions.

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<img src="imgs/unit_circle.jpg">

The unit circle is a circle with a radius of 1 unit in length—hence its imaginative name. When you work with the unit circle, you don’t use the regular and trusted Cartesian coordinate system; instead you use a polar coordinate system. The Cartesian system works great in a rectangular grid space, where a point can be located by a coordinate, such as (x, y). In a polar coordinate system, in contrast, location is specified by (r, θ), where r is the radius and θ (the Greek letter theta) is the angle of rotation. The unit circle has its origin at its center, and you measure angles of rotation beginning at the right-middle edge of the unit circle (facing 3 o’clock) and moving in a counterclockwise direction around it.

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In the unit_circle diagram, the point p is at 45° or pi / 4. You can use pi also to measure around the unit circle, as illustrated in the figure. Halfway around the circle (180°) is equal to pi radians, and all the way around the circle is equal to 2pi radians and also 0 radians, since a circle is continuous and ends where it begins. The number pi is a constant that is equal to the circumference of a circle divided by its diameter, and is approximately 3.142.