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Calculus/trigonometry unit circle

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Expert: - 12/16/2007


Question
alright i'm in precal and we're learning about the unit circle and i'm lost.First, what is the unit circle and what is it used for? I understand cos being ad/hyp and the same for sin and tan, but why is it that the cos = x and sin = y and tan = cos/sin. does the unit circle always have a radius of one or can it be more than 1, because if you take the cos(30) isn't 1/2.

Answer
Take the unit circle with radius r = 1.  sin = opposite or hypoteneuse.  The opposite side has height y and hypoteneuse r = 1, so the sin is y/1 = y.  The cos is the adj / hyp, or x/1 = x.  It is used since the hypoteneuse, which is the diagonal, is always 1 and the points on it are (cos(theta), sin(theta)) for and theta between 0 and 2*pi radians (0 to 360 degrees).

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