Instructor: Jim Jack

Trigonometry Bogus-Test

MATH 1316, Fall 2015

  1. (1 pt ea)
  2. Convert 30º to radians.
  1. Convert 570º32’ to radians.
  1. Convert 17.32º to radians.
  1. Convert radians to degrees.
  1. Convert 1 radian to degrees.
  1. (1 pt @)
  1. (5 pt) Find the latitude of Spokane, Washington, if Spokaneand Jordan Valley, Utah, (43.15ºN) are 486km apart. Use 6400km for the radius of the earth.
  1. (5 pt) A car wheel has a radius of 13 inches. How many revolutions does the wheel turn in a mile? (63360”=1mile)
  1. (5 pt) A tree 510 feet away subtends an angle of 5º. Find the height of the tree.
  1. (5 pt) A sensor light installed on the edge of a home can detect motion for a distance of 66 feet in front with a range of motion of 207º. Over what area will the sensor detect motion and become illuminated?
  1. (5 pt) Given that s is in the interval, and, find s.
  1. (5 pt) Given that s is in the interval, and, find all values of s.
  1. (5 pt) The radius of the tires of a car is 18 inches, and they are revolving at 629 revolutions per minute. How fast is the car traveling in miles per hour?
  1. (5 pt) Two pulleys of diameters 6m and 2m are connected by a belt. The larger pulley rotates 50 times per minute. Find the angular speed of the smaller pulley.
  1. (5 pt) Graph the function
  1. (5 pt)Graph the function
  1. (5 pt) Graph the function
  1. (5 pt) Graph
  1. (5 pt)For an electrical circuit, the voltage is modeled by , where t is the time in seconds. Find the amplitude, period, and frequency.
  1. (5 pt)A coil of wire rotating in a magnetic field induces a voltage given by , where t is time in seconds. Find the smallest positive time to produce a voltage of 10.
  1. (5 pt)Suppose that the average monthly low temperatures for a small town are shown in the table. Model this data using .

Month / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12
Temperature (ºF) / 19 / 27 / 38 / 45 / 57 / 62 / 65 / 58 / 51 / 41 / 33 / 25
  1. (5 pt) The minimum length L of a highway sag curve can be computed by where is the downhill grade in degrees , is the uphill grade in degrees , S is the safe stopping distance for a given speed limit, h is the height of the headlights, and α is the alignment of the headlights in degrees. Compute L for a 55-mphspeed limit, where h=1.7 ft, α=0.9º, , , and S=336 ft.
  1. (5 pt) A rotating beacon is located 14 feet from a wall. The distance from the beacon to a point on the wall where the beacon is aimed is given by , where t is time measured in seconds since the beacon started rotating. Find a forseconds.
  1. (5 pt)A weight attached to a spring is pulled down 4 inches below the equilibrium position. Assuming that the frequency of the system is cycles per second, determine a trigonometric model that gives the position of the weight at time t seconds.
  1. (5 pt) A guitar string is plucked so that it vibrates with a frequency of . Suppose the maximum displacement at the center of the string is . Find an equation of the form to model this displacement.

Answers:

  1. 9.958
  2. .302
  3. 75º
  4. 47.5º
  5. 775.7 revolutions
  6. 45 feet
  7. 7868.75’
  8. 67.3657 mph
  9. 150 rpm
  10. 70cps
  11. 2sec
  12. 728 feet
  13. 20.45 feet