Section 7-1

Section 7-1

This week in Advanced Math we started on Chapter 7. We started with section 7-1 and we learned the two units of measure are degrees and radians. We converted degrees to radians, radians to degrees, and found coterminal angles. All of these problems can be solved with the right formula. Let’s start with some example problems to understand more about what we learned.

EXAMPLE 1: The formula for converting degrees to radians is degrees multiplied by pi over 180 (degree * (pi/180)).

Convert 60 degrees to radians
1. Plug into formula - 60 * pi/180
2. Multiply to get - 60pi/180
3. Plug into your calculator - 60/180 (You do not need to plug pi into the calculator)
4. Your final answer will be - .33 as a fraction it is 1/3

EXAMPLE 2: The formula for converting radians to degrees is radians multiplied by 180 over pi (radian * (180/pi))

Convert pi/5 radians to degrees
1. Plug into formula - pi/5 x 180/pi
2. Multiply and the pi’s cancel each other out - 180/5
3. Plug into your calculator - 180/5
4. Your final answer will be - 36 degrees

Finding negative and positive coterminal angles is the simplest part of this whole section. To find a degree's positive coterminal angle, add 360. To find a negative coterminal angle you subtract 360. However, if your number is in radians you either add 2pi or subtract 2pi to get a positive or negative number. Let’s try some examples.

EXAMPLE 3: Adding and Subtracting coterminal angles with 360

Find a positive coterminal angle for -1,500
1. Add 360 to -1,500
2. Keep adding 360 to your answer until you get a positive number
3. I added 360 5 times to get a positive coterminal angle of 300

Find a negative coterminal angle for 500
1. Subtract 360 from 500
2. Keep subtracting until you get a negative number
3. I subtracted 360 2 times to get a negative coterminal angle of -220

EXAMPLE 4: Adding and Subtracting coterminal angles with 2pi

Find a positive coterminal angle for pi/4
1. Add 2pi to pi/4
2. Your answer will be 9/4 when you plug it into your calculator

Find a negative coterminal angle for pi/2
1. Subtract 2pi from pi/2
2. Your answer will be -3/2 when you plug it into your calculator

This whole section is super easy as long as you remember all over you formulas and when to add and subtract certain numbers.