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FINALTrig

# FINALTrig - MAC 1114 FINAL EXAM SHOW ALL YOUR WORK Answers...

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MAC 1114 FINAL EXAM 12/10/2007 SHOW ALL YOUR WORK. Answers without procedure will be graded zero. 1. Decide whether the following statements are True or False. a. - 3 π 2 radians = 90 d. sec( π 2 ) - 1 cos( π 2 ) = 0 b. cot 90 is not defined e. sin( θ - π 4 ) = - sin( π 4 - θ ) c. If θ = sec - 1 1 2 , then θ does not exist 2. A pendulum swings through an angle of 20 each second. If the pendulum is 40 inches long, how far does its tip move each second? 3. Without a calculator compute the value of a) (cos 23 + sin 64 ) · csc 23 and b) tan 10 - cot 80 4. Given tan θ = 3 4 , and sin θ < 0, find sin θ and cos θ . 5. a) Write the equation of a cosecant function with the following characteristics, Amplitude A = 2 3 , Period T = 3, and Phase Shift φ ω = - 1 . 5. b) Sketch the graph of such a function. Hint : first draw the corresponding sine function. 6. Find the exact value of sin(tan - 1 ( - 3)) 7. Establish the identity 1 - cos 2 θ 1 + sin θ = sin θ 8. a) Using sum and difference formulas find: sin 11 π 3 b) Using double and half angle formulas find: cos 11 . 25 (Note that 11.25 is half of 22.5)

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