sample2final (Math 121)

# sample2final (Math 121) - MATH 121 Sample Final Exam Fall...

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MATH 121 Sample Final Exam - Fall, 2006 Directions Answer all ten questions. Show your work neatly. You are not allowed to use any notes or index cards. Approximations will not be accepted, where exact answers are required. Example: 1 . 41421 . . . will not be accepted in place of the exact value 2. Cell phones or any other communication devices must be turned off during the exam. You may need the following formulas : 1. cos( x + y ) = cos x cos y sin x sin y 2. sin( x + y ) = sin x cos y + cos x sin y 3. a 2 = b 2 + c 2 2 bc cos A 4. a sin A = b sin B = c sin C Grading # points score 1 20 2 20 3 20 4 20 5 20 6 20 7 20 8 20 9 20 10 20 Total 200 1

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1. Determine the exact solutions (real and complex) of the equation: x 5 x 4 x 3 x 2 2 x = 0 . 2. Use logarithms to find the exact solution to 3 x = 4 2 x - 1 . 3. (a) Prove that 1 csc x sin x = sec x tan x . (b) Use identities to show that cos( x π ) = cos x . (c) Find the exact value of cos 7 π 12 .
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