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Trigonometry based on a unit circle and radians and trigonometry based on a right triangle.
Looking at a unit circle, cosine is the horizontal coordinate. Pi radians is halfway around the circle (180°), so the coordinate is (-1,0). Cosine(pi) = -1
Within a circle, the units used for measurement are either in degrees or in radians. In addition, radius and diameter are used, which can be in any unit of length, are important dimensions from which size, area, and circumference are obtained.
Using a meter stick, measure out a meter. Then turn pi/2 radians according to the unit circle and measure out another meter.
The period of a trigonometric function, since it depends on the angle of a ray centered in a unit circle, is 2 pi radians or 360 degrees.