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Stitz-Zeager_College_Algebra_e-book

Find the exact value of the following a arccot 3 b

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Unformatted text preview: is case is 2x − π . Loosely stated, the argument of a trigonometric function is the expression ‘inside’ the function. Example 10.5.1. Graph one cycle of the following functions. State the period of each. 1. f (x) = 3 cos π x−π 2 +1 2. g (x) = 1 2 sin(π − 2x) + 3 2 Solution. − 1. We set the argument of the cosine, πx2 π , equal to each of the values: 0, solve for x. We summarize the results below. a 0 π 2 π 3π 2 2π πx−π =a 2 πx−π =0 2 πx−π =π 2 2 πx−π =π 2 πx−π π = 32 2 πx−π = 2π 2 π 2, π, 3π 2, 2π and x 1 2 3 4 5 − Next, we substitute each of these x values into f (x) = 3 cos πx2 π + 1 to determine the corresponding y -values and connect the dots in a pleasing wavelike fashion. y x f (x) (x, f (x)) 4 3 1 4 (1, 4) 2 2 1 (2, 1) 1 3 −2 (3, −2) 4 1 (4, 1) 5 4 (5, 4) 1 2 3 4 5 x −1 −2 One cycle of y = f (x). One cycle is graphed on [1, 5] so the period is the length of that interval which is 4. 2. Proceeding as above, we set the argument of the sine, π ...
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