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SPRING 2007 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. Given that is an angle in standard position, with tan 2 and sin 0 , which quadrant contains the terminal side of
(a) I (b) II (c) III (d) IV (e) No such angle is possible.
____2. If is an angle in standard position, and the point (3, -4) is on the terminal side of , thencsc =
(a)
(b)
(c)
(d)
(e)
____3. Suppose is an angle in standard position. If
cot and the terminal side of is in Quadrant II, then (round
your answer to 3 decimal places ) (a) -1.107 (b) 63.435 (c) -63.435 (d) 116.565 (e) 120
____4. Determine ALL solutions to the equation if x^ is on the interval [^0 ,^2 ^ ): sin^0
sin 2 ( x ) x
(a)
x (b)
x (c)
x (d)
x 0 , (e)
x
____5. If )
arcsin( , find the exact value of cot . (a) 5
(b)
(c) 11
(d)
(e)
____6. A building that sits on horizontal ground has a radio antenna attached to its roof. From a point 100 meters from the base of the building, the angle of elevation to the bottom of the antenna is 30. From the same position, the angle of elevation to the top of the antenna is 40. Use this information to determine the height of the antenna. (Round to 2 decimal places.) (a) 130.54 meters (b) 17.63 m. (c) 60.89 m. (d) 26.17 m. (e) 83.91 m.
____7. Simplify the expression and write it in an equivalent form:
cot
tan cot
(a) 1150 centimeters per second (b) 50 cm./sec. (c) 46 cm./sec. (d) 575 cm./sec. (e) 2300 cm./sec. ____11. You have determined that in order to model a physical process, you need to specify a trigonometric function with the following characteristics: The amplitude is equal to 5; the period is equal to 4; and the value of the function, y, is equal to zero when X=0. Which of the following functions would satisfy these requirements?
(a) y^ ^5 sin(^4 x ) (b) )
y 5 cos( x
(c) )
y 5 sin( x
(d) )
y 5 sin( x
(e) y^ ^5 cos(^4 x )
____12. A ship leaves a port and heads due north (N 0 W) for 100 miles. It then changes course and has a bearing of N 30 W. After some time, the ship calls the port and the ship is informed that the bearing from the port to the ship is N 20 W. What is the distance from the port to the ship? (Round your answer to 2 decimal places.) (a) 146.19 miles (b) 196.96 miles (c) 287.94 miles (d) 228.89 miles (e) 498.72 miles
____13. Given the vectors v 1 2 , 3
and v 2 1 , 4
, determine the direction angle of v 1 v 2
. (Round your answer to 2
decimal places.) (a) =18.43 (b) =161.57 (c) = - 18.43 (d) =198.43 (e) =108.43
____14. The wind velocity (measured in kilometers per hours) at a weather station is represented by the vector : v^ ^30 i^ ^40 j
What is the speed of the wind? (Round your answer to 2 decimal places.) (a) 20.00 kilometers per hour (b) 50.00 km./hr. (c) 2500.00 km./hr. (d) 26.48 km./hr. (e) 3.16 km./hr.
____15. Simplify the expression and write it in an equivalent form:
cos( 2 )
sin cos
x
x x
(a)
x
x
cos
sin( ) 1
(b) sec^ x^ ^ csc x (c)
cos x sin x
(d)
cos x sin x
(e)
cos ( ) sin ( )
2 x 2 x
____16. You have purchased a tract of land that is in the shape of a triangle ABC. The following measurements are known: Angle B=35, angle C=105, and the length of side b=15 meters. You have decided to put a fence around the perimeter of the piece of land. Determine the length of fencing that will be required. (Round your answer to 2 decimal places.) Drawing a picture may help. (a) 57.07 meters (b) 65.47 m. (c) 73.45 m. (d) 94.70 m. (e) No such triangle is possible
(b) (8 points) Determine the bearing from the airport to the plane. Your answer should be in the form: N ___ ___. (Round your answer to 3 decimal places.)
- The vector representing a plane’s velocity is given by: v^ ^300 i^ ^500 j
. A wind begins blowing, and the velocity of the wind is represented by the vector: w^ ^40 i^ ^40 j
(a) (8 points) The vector representing the plane’s velocity with the wind blowing is given by v w.
Determine the
direction angle for this resultant vector. (Note: Your answer should be the measure of an angle, not a bearing.) Round your answer to 2 decimal places. A picture may be useful. (b) (6 points) By how many degrees has the plane’s course been changed from its original direction before the wind started blowing? (Round your answer to 2 decimal places.)
- From your position at the top (T) of an observation tower, you can see the entire length of a city park from its end nearest the tower (N) to the end farthest from the tower (F). The angle of depression from the top of the tower to the far end of the park is 5 , and the angle of depression from the top of the tower to the near end of the park is 15. A brochure indicates that the length of the park is 2000 meters. (Hint: Draw some lines.)
1 d 2 d 3 d 4 c 5 a 6 d 7 b 8 b 9 d 10 a 11 d 12 c 13 b 14 b 15 c 16 a Part II
- IDENTITY
- (a) Distance=360.555 miles (b) 90 – 46.102 = N 43.898 E
- (a) =64.29 (b) 64.29 - 59.04 = 5.25
- (a) 259.81 meters (b) 2980.96 meters
