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pracfinalfa07SOL

# pracfinalfa07SOL - FINAL EXAM Version 1 ~ M ATH 3 I...

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FINAL EXAM, Version 1 ~ MATH 3 12/13/2007 Instructor: Frank Bauerle, Ph.D. No books, graphing utilities or notes allowed. Show your work. Show your work. Show work. Your Name: Your TA: Max Your score Problem 1: 10 2: 3: 4: 15 5: 6: Problem 7: Problen18: 20 Problen19: 25 10: 11: 12: 13: 14: 15: TOTAL: 210 Good Luck and have a great winter break!

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-- 1. (10 points) Fill in the table and give the exact values for sino, coso and tano for o 0°, 0 30° 1 0 = 45°, 0 = 60° and 0 = 90°. Also give the radian measures of all the angles. j I 1----~ I -tCXV\ 0( ~i vl 0( COSo<, fDJ:l~t rI. ""'-~. .-. .~ J~tlJcl 0 \!CfIA. l -~o(P . T/b 30° \:::.\\. .()W --_ .. _- 45 0 ~\AS~(r Tr/'f 60 0 Tf3 I \, r. •. . 1 L.. ':~. "- .. -.~- Yv '1\ - 7 Cfo1) 1f/2 ~ ~tli.\$.ii<t4"""~.t~~ . . ; . ., - 2. (10 points) Find the reference angle, quadrant of the angle and use the reference angle principle to get the exact value of the given trig expression. (a) Quadrant of 240° = (f)}:rrr Reference angle of 240° b ()o '2. . 'toG t { {":::J tanltiClU + fA V\ (90 0 = '1 3 -57r (b) Quadrant of -6- \'f"j7 Reference angle of b csc -57r = _ _ _ ~ =_ ~ 6 ("" "IT S' J[ ..llt'\-- I~ b 3. (10 points) Find the ex~ct value of the following by using the appropriate formula. (Calculator approximations will give 0 credit, but can be used to verify your answer.). You do not need to simplify the expressions. (a) sin 15° =- S lV\ C 'f~- >O~) r;V\ ,+)0 GOJ30° - ~'k ,Ot)CDJcrro {i I £ 2 , ('fro) cor V-SO (b) sin 22.5° S)vt - ~ +~ , - ;t -, 'l- -, ={ (- i2.h_ 2- 1
4. (15 points) Consider the fUllction f(x) = ~ sin(2x 1) - 1. Find the following: (a) (1 points) The amplitude of f. 3 (b) (1 point) The vertical shift of f -1 (c) (2 points) The period of f. (d) (2 points) The phase shift of f. .f /2 (e) (6 points) The graph of f. -\ ~1C) (f) (3 points) Now graph g(x) = ~ csc(2x 1) - 1 into the same coordinate system . 2 above.

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pracfinalfa07SOL - FINAL EXAM Version 1 ~ M ATH 3 I...

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