Creating a Unit Circle Part 2 of 4

Welcome to Part 2 Changing Degrees to Radians and Radians to Degrees

Changing Degrees to Radians

The deal is this, you have probably only ever seen angles in degrees to this point in your math career. In fact, you may not have even known there was another way to measure angles, but yes, yes there is, and it is called the radian. 

From here on out, radians are going to be SUPER important, because degrees don't really translate well into working with other units, like feet and things, but radians do. In the end, we will end up using radians more in practical studies and uses of trigonometry than we will be using degrees.

The Degrees to Radians Proportion

We use proportion problems to change degrees to radians. It all starts with the fact that 180 degrees (a straight line) equals pi radians

 

To solve for radians or degrees I just set up the following proportion:

On the right side of the proportion, I have the ratio that I know, on the left side I would fill in the number that I know and solve for the one that I want.

For example, if I wanted to change 20 degrees into radians, here is how I would go about it:

So, we find that 20 degrees = 𝛑/9 radians

NOTE: YOU NEVER TURN 𝛑 INTO A DECIMAL!!!

With radians we always solve leaving 𝛑 as 𝛑. We just simplify all of the numbers around 𝛑, much like when we have a variable we are working around.

Now let's look at an example where we're solving to change 2𝛑/3 radians into degrees:

Though these efforts we see that 2𝛑/3 radians = 120 degrees

What Should I Have Filled Out In My Notes After This Section?

After you have finished this section, you should be able to fill in the  "Degrees to Radians" proportion section of your notes.

ALSO, on the table just below that section, you should be able to correctly convert all of the degrees to radians, and fill in the radians section.

Time to Practice!!

Check out this quiz, where you again get to race for your best time, but the one has some multiple choice questions!

Here is a link to the Khan Academy Practice page. The great thing about their page is it has links to their videos and other helpful information along with the practice.

This link will bring you to a worksheet you can print out and then check your answers using the attached answer key.

I NEED MORE!!!

Check out this Math BFF Video! I love my gal Nancy the MIT grad, she's got some awesome videos out there! (Full disclosure, we've never met, but I think she's awesome!)

Want to see another way to convert? Here's a website that explains another way to look at converting between the two.

The Math is Fun page will take you more in depth on what a radian is, talks more again about converting and will even give you practice problems at the bottom.