Y x final exammac1114 page 3 of 8 7 5 pts suppose sec

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Final Exam/MAC1114 Page 3 of 8 7. (5 pts.) Suppose sec θ = 4 and tan θ < 0. What is the exact value of each of the remaining trigonometric functions? cos( θ ) = tan( θ ) = sin( θ ) = csc( θ ) = cot( θ ) = 8. (4 pts.) If θ = -240°, what is the radian measure of θ as an exact multiple of π ?? θ = 9. (4 pts.) If θ = 7 π /6 in radian measure, what is the value of θ in degrees?? θ = 10. (4 pts.) If s = 5 meters is the length of an arc of a circle of radius r = 3 meters subtended by a central angle θ , what is the exact value of θ in degrees?? θ = 11. (4 pts.) If θ = 61°50 23 , convert θ to a decimal in degrees rounded to two decimal places. θ = 12. (4 pts.) If θ = 30.421°, convert θ to D°M S form with the answer rounded to the nearest second. θ =
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Final Exam/MAC1114 Page 4 of 8 13. (6 pts.) Using DeMoivre’s Theorem, find all the complex fourth roots of i. [Don’t confuse fourth roots with fourth powers!!] 14. (6 pts.) Write the equation of a sine function that has all the given characteristics: Amplitude = 4 π Period = 3 Phase Shift: -(3/4) 15. (6 pts.) Carefully sketch y = -4cos(2x + π ) through one period. You will need the amplitude, period, and phase shift to do this. Label very carefully. y x 16. (7 pts) Obtain the exact value of sin(9 π /8). Show all the uses of appropriate identities and formulas. [Hints: Reference angle? Quadrant??] sin(9 π /8) =
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Final Exam/MAC1114 Page 5 of 8 17. (5 pts.) Find the exact value of sin -1 (sin(-7 π /5)).
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