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4.1.110001 - FOR WRITING/DISCUSSION 115 Graph the function...

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Unformatted text preview: FOR WRITING/DISCUSSION 115. Graph the function y = sin(sinfi1x) for —277 S x S 271' and explain your result. 116. Graph the fimction y = sin_1(sin x) for —271 S x S 277 and explain your result. 117. Graph y = sin—1(1/x) and explain why the graph looks like the graph of y = 050*1 x shown in the Function Gallery on page 2 1 6. 118. Graph y = tan—1(1/x) and explain why the graph does not look like the graph of y = cot‘1 x shown in the Function Gallery on page 216. V RETHINKING 119.‘ The shortest side of a right triangle is 7 cm, and one of the acute angles is 64°. Find the length of the hypotenuse and the length of the longer leg. Round to the nearest tenth of a cen— timeter. 120. Suppose that a is an angle in standard position with its termi- nal side in quadrant 111 such that sin a = —5 / 6. Find exact values for cos oz and tan a. ' 121. Determine the amplitude, period, phase shift, and range for the function‘y = 5 sin(4x — 71') — 3. yO‘P QUIZ 4.1 Find the exact value. 1. sin—1(—l) 2. sin’1(1/2) 3. arccos( — l) 4. arctan( —- l) 5. itan(arcsin(il/2)) 6. sin’1(sin(37T/4l)) 4.1 Linking Concepts .221 122. Determine the period, asymptotes, and range for the function y = 3csc(1Tx — 77) + 2. 3 csc2 (x) ' 123. Simplify the expression 3 — 124. Simplify the expression (sinx + cos x)2 — sin(2x). THINKING OUTSIDE THE BOX XXVII Lucky Lucy Ms. Willis asked Lucy to come to the board to find the mean of a pair of one-digit positive integers. Lucy slowly wrote the numbers on the board. While trying to think of what to do next, she rested the chalk between the numbers to make a mark that looked like a decimal point to Ms. Willis. Ms. Willis said “correct” and asked her to find the mean for a pair of two-digit positive inte- gers. Being a quick learner, Lucy again wrote the numbers on the board, rested the chalk between the numbers, and again Ms. Willis said “correct.” Lucy had to demonstrate her ability to find the mean for a pair of three—digit and a pair of four-digit positive inte- gers before Ms. Willis was satisfied that she understood the con- cept. What four pairs of integers did Ms. Willis give to Lucy? EX— plain why Lucy’s method will not work for any other pairs of one-, two-, three-, or four-digit positive integers. Find the exact value for x in the interval [0, 77/ 2] that satisfies each equation. 7. sin(x) = V2/2 8. cos(x) = 0 9. tan(x) = l f ...
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