Measurement of Angles!

--So because of the horrible weather that we are supposed to be getting soon and continuing throughout the weekend, I've decided to do my blog a little early just incase the electricity would happen to go out.. lol (:

1. Degrees can be broken down into minutes (') and seconds ('').

• To convert to minutes, you take what is behind the decimal and multiply it by 60.
  


• To convert to seconds, you take what is behind the decimal in the minutes and multiply it by 60.
  


• To convert minutes and seconds to degrees, use the formula:
  degrees+minutes/60+seconds/360
  

2. Radians are the preferred way to measure angles, ALL formulas require radians.

• To convert degrees to radians, use the formula: degrees(pi/180).
  


• To convert from radians to degrees, use the formula: radians(180/pi).
  

3. Coterminal angles are like non-reduced fractions.

• Degreesplus/minus360degrees(n)=coterminal angle
  


• n can be any whole number
  


• radiansplus/minus2pi(n)=coterminal angle
  


• n can be any whole number
  

4. In the Formula s=r(theta), s=arc length, r=radius, theta=central angle in radians.

• s and r must have the same units
  

Example 1:

Convert 14.33degrees to degrees minutes and seconds.

a. .33(60)= 19.8

b. .8(60)= 48

14degrees19'48''

Example 2:

Convert each degree measure to radians.

a. 315degrees

315degrees(pi/180)= 7pi/4

b. 225degrees

225degrees(pi/180)= 5pi/4

c. 15degrees

15degrees(pi/180)= pi/12

d. -45degrees

-45degrees(pi/180)= -pi/4

Example 3:

Convert each radian measure to degrees.

a. pi

pi(180/pi)= 180 degrees

b. -3pi/2

-3pi/2(180/pi)= -270 degrees

c. 2pi/3

2pi/3(180/pi)= 120 degrees

d. 7pi/6

7pi/6(180/pi)= 210 degrees

Example 4:

Find two angles, one positive and one negative, that are coterminal with each angle.

a. 28.5 degrees

28.5+360= 388.5 and 28.5-360= -331.5

b. 116.3 degrees

116.3+360= 476.3 and 116.3-360= -243.7

c. -60.4 degrees

-60.4+360= 299.6 and -60.4-360= -420.4

d. -315.3 degrees

-315.3+360= 44.7 and -315.3-360= -675.3

P.S. I don't know why it spaced so much. Every time I try to fix it, it goes right back.
Sorry about that!