Download Math 141/142 Trigonometry Final Exam Fall 1999 and more Exams Trigonometry in PDF only on Docsity! Math 141/142 PRINT YOUR NAME: Fall 1999 Trigonometry Final Exam SIGN YOUR NAME: SECTION #: For problems 1-12, write your answer in the blank provided. Include units if appropriate. For multiple choice problems, write the letter corresponding to your answer. No partial credit will be awarded for these problems. Each problem is worth 5 points. 1. If sinx = √ 3 2 and cotx < 0, find the exact value of tan(x). 1. 2. Find the radian measure of a central angle θ opposite an arc s = 27 meters in a circle of radius r = 18 meters. 2. 3. Given that a = 22, b = 35, and c = 27, find the measure of angle α to the nearest degree. 3. a c b α β γ 4. At a certain time of day, the Washington Monument casts a shadow 790 feet long. From the tip of the shadow, the angle from the horizontal to the top of the monument is 35◦. Use this information to find the height of the monument to the nearest foot. 4. 5. The function y = 3 sin(4x) + 2 cos(6x) is (a) a periodic function of period π3 . (b) a periodic function of period π2 . (c) a periodic function of period π. (d) a periodic function of period 2π. (e) not a periodic function. 5. 6. Suppose secx = −53 with π < x < 3π2 . Find the exact value of sin(x2 ). You do not have to simplify your answer. 6. 7. tanx(cscx cosx− sinx cosx) = (a) sin2 x (b) cos2 x (c) tan2 x (d) cot2 x (e) sec2 x (f) csc2 x 7. 8. Find all solutions of the equation tan θ = 2.79 on the interval [0, 2π], accurate to two decimal places. 8. 9. An object hangs from a spring attached to the ceiling. If the object is pulled down to the starting position and released, it moves according to the law y(t) = A cos(Bt), where y is the vertical position of the object and t is time in seconds. The position of the object at rest is y = 0. Suppose at time 0 the object is pulled down 4 cm (y = −4) and released. After 1.5 seconds the object returns to the starting position. Find A and B. 9. 10. Given that the point (−3, 4) is a point on the terminal side of an angle θ, find the exact value of sin θ. 10. 11. Given that α = 35◦, a = 60, and b = 70, how many triangles can be constructed? a c b α β γ (a) none (b) one (c) two (d) three 11. 12. Find all exact solutions of the equation 1 + 2 cosx = 0 on the interval [0, 2π]. 12. For problems 13-16 below, you must show all of your work in the space provided. Partial credit is possible on these problems. Each problem is worth 10 points. 13. Suppose tanx = 512 with π < x < 3π 2 , and sin y = − 35 with 3π2 < y < 2π. Find the exact value of cos(x− y). Be sure to show all of your work. Simplify and circle your answer.
