Degrees, Minutes and Seconds.

1. Degrees:

Degrees can be broken down into minutes(') and seconds(").
a. To convert to minutes, take what's behind the decimal and multiply by 60.

b. To convert to seconds, take what's behind the decimal in the minutes and multiply by 60.

c. To convert from minutes and seconds to degrees, use this formula:

[degrees + min/60 + sec/3600 = final degree value]

2. Radians:

Radians are the preferred way to measure angles. All formulas require radians.

a. To convert degrees to radians, use this formula:

[degrees x 180/pi]

To use this formula, simply type in the degrees/180 in your calculator, then put pi beside it.

b. To convert from radians to degrees, use this formula:

[rads x 180/pi=degrees]

3. Coterminal angles

Coterminal angles are like non-reduced fractions in that that several coterminal angles can mean the same thing, even though they have the same numbers.

a. The formula for coterminal angles is:

[degrees + or - 360 degrees x n = coterminal angle]

In this formula, n can be any whole number.

b. The other formula is:

[rads + or - 2(pi)n = coterminal angle]

In this formula, n can be any whole number.

(Basically, you just add or subtract 360 until you get a positive or negative number. This works because every time you add or subtract 360, you're giving the angle a full turn, making it the same exact angle.)

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Examples:

1. Convert 12.22 degrees to degrees, minutes, and seconds.

a. .22 x 60 = 13.2'
b. .2 x 60 = 12"

12 degrees 13' 12"

2. Convert 20 degrees 20' 6" to degrees

c. 20 + 20/60 + 6/3600 = 20.335 degrees

3. Convert 196 degrees to radians.

196 x pi/180 = 49/45(pi)

4. Convert 3(pi)/4 to degrees.

3(pi)/4 x 180/pi = 135 degrees

5. Convert 1.35 rads to degrees, minutes, and seconds.

1.35 x 180/pi = 77.349 degrees

.349 x 60 = 20.94'

.94 x 60 = 56.4"

77 degrees 20' 56"

6. Find a positive coterminal angle to -60 degrees.

-60 degrees + 360 degrees = 300 degrees

7. Find a negative coterminal angle to 1050 degrees.

1050 degrees - 1080 degrees = -30 degrees

8. Find a coterminal to pi/4 (2(pi) = 360 degrees in rads)

9/4(pi).