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Published byReginald Parrish Modified over 9 years ago
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5.2 Trigonometric Functions: Unit Circle Approach
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The unit circle is a circle whose radius is 1 and whose center is at the origin. Since r = 1: becomes
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(0, 1) (-1, 0) (0, -1) (1, 0) y x
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(0, 1) (-1, 0) (0, -1) (1, 0) y x P = (a, b)
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Let t be a real number and let P = (a, b) be the point on the unit circle that corresponds to t. The sine function associates with t the y-coordinate of P and is denoted by The cosine function associates with t the x-coordinate of P and is denoted by
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If the tangent function is defined as Ifthe secant function is defined as the tangent function is defined asIf
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the cotangent function is defined as
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(0, 1) (-1, 0) (0, -1) (1, 0) y x P = (a, b)
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If radians, the six trigonometric functions of the angle are defined as
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y x r a b
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Theorem
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P=(a,b) (5, 0) Find the exact value of the remaining five trigonometric functions, given:
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meaning
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gives
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P= (0,1) x y undefined
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P= (1, 0) P= (a, b) x undefined
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a =1
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