QED Insight

The two most commonly used measures for angles are degrees and radians. There are 360 degrees in a full circle (a right angle is 90 degrees), and $latex 2\pi$ radians in a full circle (there are $latex \pi/2$ radians in a right angle), so there are about 57 degrees in a radian.

Students typically learn about degrees before they learn about radians, which brings up the question: Why learn about radians if degrees are good enough for measuring angles? There are two reasons, but both are grounded in the fact that the radian is a unitless measure, which I’ll explain in the following paragraph.

The radian is defined to be (see the diagram) the ratio of the length of the arc of a circle (indicated by $latex s$ in the diagram) to the length of the radius of the circle (indicated by $latex r$ in the diagram), where each length…

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