Trigonometry/For Enthusiasts/Degrees Minutes and Seconds

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1. Explain the term coterminal.
2. What are complementary angles?
3. What are supplementary angles?

Angle Addition[edit]

In the following problems, find the sum A+B and the difference A-B of the two given angles.

4. A = 38^{\circ}15^{\prime} B = 17^{\circ}5^{\prime}
5. A = 98^{\circ}41^{\prime}42^{\prime\prime} B = 50^{\circ}25^{\prime}55^{\prime\prime}
6. A = 150^{\circ}2^{\prime}1^{\prime\prime} B = 266^{\circ}44^{\prime}9^{\prime\prime}
7. A = -18^{\circ}11^{\prime}19^{\prime\prime} B = 38^{\circ}17^{\prime}17^{\prime\prime}
8. A = 138.7222^{\circ} B = 21.9111^{\circ}
9. A = 335.8500^{\circ} B = -34.9500^{\circ}
10. A = -48.8^{\circ} B = 336.4556^{\circ}
11. A = -17.6056^{\circ} B = -87.2694^{\circ}

Convert To Decimal[edit]

In the following problems convert the given angle in degrees, minutes, seconds to decimal degrees.

12. 38^{\circ}15^{\prime}
13. -71^{\circ}22^{\prime}43^{\prime\prime}
14. 428^{\circ}0^{\prime}18^{\prime\prime}
15. 180^{\circ}17^{\prime}38^{\prime\prime}

Convert To Degree-Minutes-Seconds[edit]

In the following problems convert the given angle in decimal degrees to an angle in degrees, minutes, seconds.

16. 279.6938^{\circ}
17. -23.3040^{\circ}
18. 167.0030^{\circ}
19. 316.2575^{\circ}

Draw The Angle[edit]

Example: The point (5,6) is plotted and the line is measured to be about fifty degrees with the x-axis.

On paper, draw the following angle. If the angle is negative or larger than 360^{\circ}, convert it to an angle between 0^{\circ} and 360^{\circ}.

20. 72^{\circ}
21. 400^{\circ}
22. -42^{\circ}
23. -395^{\circ}

On graph paper plot the following points and measure the angle with a protractor.

24. \left(7,2\right)
25. \left(-5,7\right)
26. \left(-2,-8\right)
27. \left(1,-5\right)

Real World[edit]

28. During an orienteering competition, you are headed in a compass direction of 38^{\circ}29^{\prime}.
  You find that you need to head in the direction of 298^{\circ}4^{\prime}.
  How far must you change your course in order to travel in the new direction.
29. Tuning the engine of your early model Chevy Camaro, you find the sparkplug fires at 1^{\circ}
  after the flywheel reaches the top position. You want the sparkplug to fire at 5^{\circ}
  before it reaches the top. How many degrees must you adjust the timing so that it fires correctly?
30. If your bicycle wheel spins around twice, how many degrees has it rotated?
31. A radar antenna rotates twice each minute. How many degrees will it rotate in an hour and a half?