7-1 Measurement of Angles

7-1 Measurement of Angles
This week in Advanced Math we covered Chapter 7. Our first section, 7-1, taught us how to find the measure of an angle in either degrees or radians and to find coterminal angles. As we learned, there are two units of measurement: degrees and radians.

First, lets see how you would convert degrees to radians.
The formula for converting degrees to radians is (degrees x pi/180).
EXAMPLE 1: Convert 36 degrees to radians (to the nearest hundredth).
1. Plug into formula - 36 x pi/180
2. Multiply to get 36pi/180
3. Plug 36pi/180 into your calculator.
4. You round to get .63
EXAMPLE 2: Convert 270 degrees to radians (give answer in terms of pi).
1. Plug into formula - 270 x pi/180
2. Multiply to get 270pi/180
3. 270 and 180 are divisible by 90 so your answer will be 3pi/2.

Now that we've gone over degrees to radians, lets try radians to degrees.
The formula for converting radians to degrees is (radians x 180/pi).
EXAMPLE 1: Convert 2pi/3 to degrees.
1. Plug into formula – 2pi/3 x 180/pi
2. Pi cancels out.
3. Then, multiply 2/3 x 180
4. Your answer is 120 degrees.
EXAMPLE 2: Convert 2.5 x 180/pi to degrees (give answer to nearest tenth of a degree).
1. Plug into formula – 2.5 x 180/pi
2. Plug 2.5 x 180/pi into your calculator
3. Round and your answer will be 143.2 degrees

Along with these two formulas, we were also taught how to find negative and positive coterminal angles. It may sound difficult, but we all know that it’s pretty simple.
To find a positive coterminal angle, add 360. To find a negative coterminal angle, subtract 360. Let’s try that.
EXAMPLE 1: Find a positive and negative coterminal angle to -1000 degrees.
1. To find a positive coterminal angle, add 360 until your answer is positive.
2. You had to add it three times to get 80 degrees. There is your positive.
3. Now, subtract 360 from -1000.
4. Your answer should be -1360.
**** When finding coterminal angles, your answers will vary. Just make sure it’s positive when it should be and negative when it should be.


The key to understanding Chapter 7 is learning your formulas! It’s much easier to learn when you know what you’re plugging your numbers into :)