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Pre-Calc Exam Notes 11

# Pre-Calc Exam Notes 11 - Trigonometric Functions of an...

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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 the
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