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FALL 2006 MATH 1060 FINAL EXAM Name___________________________ PART I: MULTIPLE CHOICE Each problem has only one correct answer. Place your answer in the space provided. Each problem is worth 9 points. ____1. If
cos( ) and tan( ) 0 , then sin( )
(a)
(b)
(c)
(d)
(e)
____2. If is an angle in standard position, which of the following points is on the terminal side of if
tan( ) and
cos( ) 0?
(a) (5, - 12) (b) (5, 13) (c) (12, - 5) (d) ( - 5, 12) (e) ( - 5, 13)
____3. Suppose is an angle in standard position that satisfies the following conditions: sec(^ ^ )^2 and 0 .
Determine the radian measure of the reference angle for .
(a)
(b)
(c)
(d)
(e)
____4. Determine ALL solutions to the equation if x is on the interval [ 0 , 2 ):cos x sin x cos x
(a)
x (b)
x (c)
x (d)
x 0 , (e)
x
____5. Evaluate: sin(arctan(^1 ))
(a) 2
(b)
(c)
(d)
(e)
____6. An air traffic controller sitting at a radar station on the ground sees a plane that she determines is directly above a town that is 5 miles from the radar (measured along the ground). The pilot tells the controller that the plane’s altitude is 3 miles at that point in time. Determine the angle of elevation from the air traffic controller to the plane. (Round to 2 decimal places.) (a) 59.04 (b) 30.96 (c) 36.87 (d) 53.13 (e) 25.28 ____7. Simplify the expression and write it in an equivalent form: csc x sec x cot x
(a) 32.02 miles (b) 57.74 miles (c) 60.62 miles (d) 52.5 miles (e) 53.28 miles ____11. The temperature at a location in the desert, measure in degrees Fahrenheit (F), fluctuates in a cyclical manner that we wish to represent with a trigonometric function. Over a 24-hour cycle, the temperature varies from a maximum of 90F at time t= (12:00 Noon) to a minimum of 30F at time t=12 (12:00 Midnight); the temperature returns to 90F at time t=24 (12:00 Noon). Which of the following functions would be an appropriate model to describe the temperature at time t hours from 12:00 Noon on a given day?
(a) )
F 60 30 sin( t
(b) )
F 60 30 cos( t
(c) F 60 30 cos( 12 t )
(d) )
F 60 30 sin( t
(e) )
F 90 60 sin( t
____12. Two vectors are used to represent the forces being applied to an object. The vectors are given as: F 1 3 i 4 j
and
F 2 3 j
. What is the direction angle for the vector F 1 F 2?
(Round to 2 decimal places.)
(a) 23.20 (b) 33.69 (c) 66.80 (d) 56.31 (e) 1.17 ____13. A force with a magnitude of 1000 pounds is applied with a direction angle of 120. Which of the following vectors would be an appropriate description of this force?
(a) (^) F i j 2
(b) (^) F i j 2
(c) F 1000 i 1000 3 j (d) F 500 i 500 3 j (e) 500 i 500 3 j
____14. Simplify the expression and write it in an equivalent form: ^2 cos ( )
sin( 2 )
x
x
(a) cot x (b) (^2) cot x (c) cos x cot x (d)
x
x
cos
1 sin
(e)
x
x
cos
2 sin
____15. Given a triangle ABC with a=80 feet, b=100 feet, and angle B=148, find the length of side c. (Drawing a picture may help.) Round your answer to 2 decimal places. (a) 26.87 feet (b) 22.73 feet (c) 25.08 feet (d) 100.00 feet (e) No such triangle is possible ____16. Given a triangle ABC with side b=15 feet, c=20 feet and angle B=80, determine the area of the triangle. (Drawing a picture may help.) Round your answer to 2 decimal places.
(a) (10 points) Determine the magnitude and the direction angle of the resultant vector representing the force on the object. (Hint: Sketch a graph of the vectors.) Round your answer to 3 decimal places. (b) (4 points) Determine the component form of a unit vector that is in the same direction of the resultant vector that you found in part (a). Round your answer to 3 decimal places.
- On one side of a communication tower BC, which rises perpendicular to the ground, two support wires will be attached to the tower. Wire AB is 180 feet long and the angle of elevation from its attachment with the ground at point A to the top of the tower is 40. A second wire, DE, is to be attached to the tower at point D, which is 40 feet below the top of the
tower at point B. It is required that this wire be attached to the ground at point E such that the angle of elevation from its attachment at point E to point D is 50. (a) (7 points) How long should the second wire be so that it can attach at points D and E as described above? (Round to 2 decimal places.) (b) (7 points) In order to move vehicles and equipment around the base of the tower, the operations manager needs to know the distance between the 2 points of attachment for the wires, points A and E. Determine the length AE. (Round to 2 decimal places.)
- A hiker leaves point A and heads due east for 10 miles to point B. She then turns and hikes 12 miles to point C. From there, she hikes 18 miles back to point A.
Part I 1 c 2 a 3 d 4 c 5 e 6 b 7 c 8 a 9 d 10 e 11 b 12 c 13 d 14 a 15 b 16 e Part II 1 IDENTITY 2 (a) Magnitude=557.260 pounds; Direction angle=122.571 (b) - .538, .843 3 (a) Length DE = 98.82 feet; (b) Length AC = 137.89 ft.; length EC = 63.52 ft.; Length AE = 74. 4 (a) Angle B = 109.47; (b) 109.47 - 90 = 19.47 N 19.47 E
