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The Complete Idiot's Guide to Trigonometry by Izolda Fotiyeva, Dmitriy Fotiyev

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Measuring Angles

So far we have mostly discussed acute angles and their trigonometric functions. We also touched on obtuse angles and some of their sines and cosines. But at this point, you might be wondering how to determine the sine of 500º or the cosine of 1,000º.

What do these large measures of degrees measure? Certainly, they cannot measure any of the angles in a triangle, because these can be only between 0º and 180º (even though nobody has ever seen an angle in a triangle with a measure of 180º). They cannot measure any central angles or arcs in a circle, either, because these can be only between 0º and 360º.

Imagine yourself standing in front of a carousel that runs around a circle. Suppose also that your younger sibling sits on a toy ...

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