Unformatted text preview: Trigonometric Functions of an Acute Angle • Section 1.2 11 We now know the lengths of all sides of the triangle △ ABC , so we have: cos A = adjacent hypotenuse = radicallow 5 3 tan A = opposite adjacent = 2 radicallow 5 csc A = hypotenuse opposite = 3 2 sec A = hypotenuse adjacent = 3 radicallow 5 cot A = adjacent opposite = radicallow 5 2 You may have noticed the connections between the sine and cosine, secant and cosecant, and tangent and cotangent of the complementary angles in Examples 1.5 and 1.7. General izing those examples gives us the following theorem: Theorem 1.2. Cofunction Theorem: If A and B are the complementary acute angles in a right triangle △ ABC , then the following relations hold: sin A = cos B sec A = csc B tan A = cot B sin B = cos A sec B = csc A tan B = cot A We say that the pairs of functions { sin,cos }, { sec,csc }, and { tan,cot } are cofunctions . So sine and cosine are cofunctions, secant and cosecant are cofunctions, and tangent and cotangent are cofunctions. That is how the functions cosine, cosecant, and cotangent got thecotangent are cofunctions....
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 Fall '11
 Dr.Cheun
 Calculus

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