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 onedigit 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 twodigit 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 fourdigit 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 fourdigit 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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 Summer '11
 BryanWhite
 Trigonometry

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