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Stitz-Zeager_College_Algebra_e-book

# We need to argue that each of these angles t into a

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Unformatted text preview: cotangent. We 10.7 Trigonometric Equations and Inequalities 731 x) x) choose3 to use the quotient identity cot(3x) = cos(3x) . Graphing y = cos(3x) and y = 0 (the sin(3 sin(3 x-axis), we see that the x-coordinates of the intersection points approximately match our solutions. 4. To solve sec2 (x) = 4, we ﬁrst extract square roots to get sec(x) = ±2. Converting to cosines, 1 π we have cos(x) = ± 2 . For cos(x) = 1 , we get x = π + 2πk or x = 53 + 2πk for integers k . 2 3 2π 4π 1 For cos(x) = − 2 , we get x = 3 + 2πk or x = 3 + 2πk for integers k . Taking a step back,4 π π we realize that these solutions can be combined because π and 43 are π units apart as are 23 3 5π π 2π and 3 . Hence, we may rewrite our solutions as x = 3 + πk and x = 3 + πk for integers k . Now, depending on the integer k , sec π + πk doesn’t always equal sec π . However, it is 3 3 true that for all integers k , sec π + πk = ± sec π = ±2. (Can you show this?) As a result, 3 3 π sec2 π + πk = (±...
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