oddans53 - Odd-Numbered Answers to Exercise Set 5.3: Graphs...

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Odd-Numbered Answers to Exercise Set 5.3: Graphs of the Tangent, Cotangent, Secant, and Cosecant Functions Math 1330, Precalculus The University of Houston Solutions to Chapter 5 Exercises 1. (a) x () tan yx = x tan = 0 0 2 π Undefined 12 0.27 7 12 3.73 6 0.58 2 3 1.73 4 1 3 4 1 3 1.73 5 6 0.58 5 12 3.73 11 12 0.27 0 (b) (c) (d) Domain: 35 , , ,... 22 2 xx πππ ⎧⎫ ≠± ± ± ⎨⎬ ⎩⎭ Range: , −∞ ∞ (e) Period: Continued in the next column… (f) Answers vary. Following are some intervals on which ( )( ) tan f = is increasing. (Any one interval is sufficient.) , ππ ⎛⎞ ⎜⎟ ⎝⎠ 3 , , 3 , −− 53 , etc… There are no intervals on which ( ) ( ) tan f = is decreasing. 3. (a) x ( ) sec = x ( ) sec = 0 1 1 6 1.15 7 6 1.15 4 1.41 5 4 1.41 3 2 4 3 2 2 Undefined 3 2 Undefined 2 3 2 5 3 2 3 4 1.41 7 4 1.41 5 6 1.15 11 6 1.15 2 1 (b) Continued in the next column… −2π −3π/2 −π −π/2 π/2 π 3π/2 −4.0 −3.0 −2.0 −1.0 1.0 2.0 3.0 4.0 x y π/12 π/6 π/4 π/3 5π/12 7π/12 2π/3 3π/4 5π/6 11π/12 π −4.0 −3.0 −2.0 −1.0 1.0 2.0 3.0 4.0 x y 2π/3 5π/6 π 7π/6 4π/3 3π/2 5π/3
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oddans53 - Odd-Numbered Answers to Exercise Set 5.3: Graphs...

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