7-1

7-1
I am going to show you how to convert degrees to radians, and radians to degrees.

Degrees to Radians
a.) To convert (degrees) to radians the formula is degrees x pie/180
- To type this into a calculator you would input (degrees/180) which would give you a fraction. Then put (pie) next to it as the final answer.

Example:
Convert 300 degrees to radians.

1. Plug 300 degrees into the formula. 300 x pie/180.


2. Enter 300/180 into your calculator: 300/180= (5/3)


3. Put (pie) next to fraction.


4. Final answer should look like this: (5/3)pie

Radians to degrees

a.) to convert radians to degrees, the formula is rad x 180/pie (Pie will cancel)

Example

Convert (5/4)pie to degrees

1. Plug (5/4)pie into formula


2. (5/4)pie x 180/pie


3. The (pie) cancel and you get left with: (5/4) x 180


4. The answer would be 225 degrees

I am so happy and filled with joy that i could help my fellow human beings. Tune in next week so I can help you with something else Mrs. Robinson teaches me. Boy o boy i cant wait. See you there:)

7-1 Degrees and Radians

This section is all about conversions. First we will be converting degrees to minutes and seconds. Then we will be converting degrees to radians and radians to degrees.

1. Converting degrees to minutes and seconds
You only have to convert degrees to minutes(') and seconds(") if it is a decimal.

• When converting to minutes you take what is behind the decimal in the degrees and multiply it by 60. (If you still have a decimal then you have to then convert to seconds)


• When you convert to seconds you take the numbers that are behind the decimal in the minutes and multiply by 60. (If you still have a decimal you just drop of the numbers behind the decimal when you right your answer)

2. Converting degrees to radians

• All you have to do to convert degrees to radians is plug into the formula: degrees * pi/180 (you can do this easily by entering in your calculator, degrees/180, change the answer to a fraction, and put pi on the side of it.

3. Converting radians to degrees

• To convert from radians to degrees, you plug into the formula rads * 180/pi (if the radians have pi in it then pi will cancel each other out)

Examples:

1.Convert 75.63 degrees to minutes and seconds:

.63*60=37.8' .8*60=48"

The final answer is 75 degrees 37' 48"

2. Convert 212 degrees to radians:

212 degrees * pi/180=(53/45) pi

The answer is (53/45) pi

3. Convert (2 pi/3) to degrees:

(2 pi/3)*(180/pi)=((2*180)/3)=(360/3)=120 degrees

The answer would be 120 degrees

-Braxton-

7-2

Hey Brob its Danielle from first hour again. Im gonna come see you at lunch cause i think your email hates my email cause it never sends so i"m stuck using Sarahs again.

*Formula 1: k=(1/2)r^2(theta)

-k is the area of a sector

-r is the radius

-s is the arc length

-theata is the central angle

*Formula 2: k=(1/2)rs

-r is the radus

-s is the arc length

-k is the area of sector

*Formula 3: s=r(theta)

-r is the distance between two objects

- theta is the apparent size

-s diameter fo an object

Example 1: A sector of a circle has a radius 6 cm and central angle 0.5 radians. Find its arc length and area.

-r= 6cm

-theta= 0.5

-s= ?

k= ?

-I would use forumula 1 to find k. k=(1/2)r^2(theta)

k=(1/2)(6)^2(0.5) *You multiply them all

k=9 cm

-Now i would use formula 2 to find s. k=(1/2)rs

9=(1/2)(6)s *First you multiply 1/2 times 6 which will give you 9=3s and then you divide 3 by 9.

s= 3 cm

Example 2: A sector of a circle has arc length 2 cm abd central angle 0.4 radians. Find its radius and area.

-s= 2cm

-theta= 0.4

-k= ?

-r= ?

-I would use formula 3 first to dins r. s=r(theta) *To find r it would be r= s/theta

r= 2/0.4 r= 5 cm

- Now i would use formula 1 to find k. k=(1/2)r^2(theta)

k=(1/2)(5)^2(0.4) k= 5 cm

--Danielle

7-1 Degrees and Radians

In this section we will be learning how to convert degrees into minutes and seconds, convert radians to degrees, and degrees to radians.

êThe first thing we’re going to learn is how to convert degrees into minutes and seconds.

1. The first thing you are going to do is take what is behind the decimal and multiply it by 60.
2. Next, to convert to seconds, you take what is behind the decimal in the minutes and multiply that by 60.

êêThe second thing we’re going to be learning is how to convert a degree into a radian.

1. Use the formula degree x Pi/180.

HINT: Type in the degree/180 into you’re calculator, put it into a fraction, and put Pi beside it.

êêêThe third and final thing we are going to be learning today is how to convert radians into degrees.

1. Use the formula Rads x 180/Pi=degree.

HINT: Pi will cancel

Now, I am going to show you an example of each.

êExample 1: Convert 16.73º to minutes(‘) and seconds(“)

1. .73 x 60 = 43.8
2. .8 x 60 = 48

You’re answer would be 16º43’48”

êêExample 2: Convert 24º into Radians.

1. 24/180= 2/15 = 2Pi/15

You're answer would be 2Pi/15

êêêExample 3: Convert Pi/2 into degrees.

1. Pi/2 x 180/Pi =90º

You're answer would be 90º

--Carley--

7-2

In this section, there are three formulas you can use:

• K = 1/2r^2theta (theta is a circle with a line through it, but I don't know how I could put that on here so...i just wrote it out). K stands for the area of a sector. R stands for the radius and Theta stands for the central angle.
• K = 1/2rs. In this formula, R stands for the radius and S stands for the are length.
• S = rTheta. S is the are length, R is the radius, and Theta is the central angle.

Apparent Size:

• S = rTheta: R is the distance between two objects, Theta is the apparent size, and S is the diameter of the object.

Ex. A sector of a circle has an arc length of 10cm and an area of 55cm^2. Find the radius and the measure of its central angle.

1. First you need to identify the things you already have and what you need.

• S = 10cm
• K = 55cm^2
• R= ?
• Theta = ?

2. Now you need to figure out what formula you can use for this word problem.

• You can use K = 1/2rs.
• You can also use S=rtheta.

3. Now you need to plug in the numbers you have into the first problem.

• Since you are trying to find your Radius, you need to solve for R.
• You will end up with 2k = rs. (you divided by 2 on each side to get that).
• Now you need to get R on the side where the 2k is. You divide each side by S. You end up with R = 2k/s.
• Now you plug in your numbers. R = 2(55)/10.
• Your final answer is R = 11.

4. Now you have to find Theta.

• Use the equation S= rtheta.
• You have to solve for Theta. So your equation will now be: Theta = S/R.
  
• You plug in your Radius and arc length into the problem.
• Theta = 10/11
• Final answer: Theta = 10/11 rads.

-Amber :)

7-1 Measurement of Angles

Two ways to measure angles are by using degrees and radians:


1) You can break down degrees into minutes(') and seconds(").

-If you're converting degrees to minutes, you take all numbers behind the decimal, and multiply that by 60.

-If you're converting degrees to seconds, you take all the numbers behind the decimal in what you got for minutes, and multiply that by 60.

-If you want to convert minutes and seconds back to degrees, you use the following equation:
degrees + (min/60) + (seconds/3600)

Ex 1: Convert 15.33 degrees to degrees, minutes, and seconds.

a) .33 X 60 = 19.8'

b) .8 X 60 = 48"

answer = 15 degrees 19' 48"

2) Radians are the recommended way to measure angles. All formulas require radians.

-To convert degrees to radians: degree(x)(pie/180)

-To convert from radians to degrees: radians(x)180/pie)

*pie will cancel out

Ex 2: Convert 195 degrees to radians.

a) 195 X (pie/180)

answer = (13/12)pie

And those are some examples of how to measure angles.-Jordan Duhon:)

7-1/ Degrees and Radians

So I'm going to be explaining a few different things. The first thing is how to break down degrees into minutes and seconds. The others are how to convert degrees into radians and converting radians into degrees.

*Breaking down degrees into minutes and seconds have 2 easy steps:

1. The first thing you want to do is convert the degree they give you into minutes. To do this you would take what is behind the decimal of the degree and multiply it by 60.
2. The next step is to then convert to seconds. Would would then take what is behind the decimal of the minutes and mulitply by 60.

NOTE: The only time you would ever break down a degree into minutes and seconds would be when the degree they give you has a decimal. The point of breaking it down is to get a number that isn't a decimal.

**Now we are going to convert degrees into radians. You can do this in one simple step.

1. The formula for converting degrees into radians is: degrees X Pi/180=radian. This formula is very simple. If you were using a calculator you would plug in the degrees and divide it by 180. You would then convert that answer into fraction form and put the pi symbol besides it.

***I am now going to tell you how to convert radians back into degrees. You can do this in one simple step too.

1. The formula for converting radians back into degrees is: radian X 180/Pi=degree. This formula is once again very simple. If your radian has a Pi symbol, then they were cancel each other out and you would simply divide the radian by 180. If your radian doesn't have a Pi symbol, then you would still divide the radian by 180 but now you would just add the Pi symbol to the side of your answer.

NOTE: Not all radians have Pi symbols, this is why it is very important to know that degrees will always have the degree symbol. You need to know that to be able to tell radians and degrees apart.

Okay, so now I am going to give you an example of each of the problems I explained above. Note that I am going to use the star symbols on side of each new problem so you know which one I am working. I am also going to number each step I do to match the ones above.

*Example 1: Break down the degree given into minutes and seconds.

14.21 degrees

1. .21 x 60= 12.6
2. .6 x 60= 36

Your answer would then be: 14 degrees 12 minutes and 36 seconds.

**Example 2: Convert the degree given into a radian.

315 degrees

1. 315 x Pi/180= 7/4 Pi

Your answer would then be: 7/4 Pi

***Example 3: Convert the radian given into a degree.

4 Pi/3

1. 4 Pi/3 x 180/Pi= 240 degrees

Your answer would then be: 240 degrees.

And that is pretty much it!

--Halie :)