Trigonometry/For Enthusiasts/Degrees Minutes and Seconds

Vocabulary

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

Angle Addition

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

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

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

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.	$(7,2)$
25.	$(-5,7)$
26.	$(-2,-8)$
27.	$(1,-5)$

Real World

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?