StudySmarter - The all-in-one study app.
4.8 • +11k Ratings
More than 3 Million Downloads
Degrees are the well-known angle measurement that can be used in trigonometry. An alternative is the concept of radians.
Radians are an alternative angle unit that make more sense if we consider a circle – so let's do that.
STEP 1: Let's start by drawing a circle with a unit radius (radius of 1).
A general unit circle
STEP 2: Let's start moving this radius by angle.
STEP 3: Now let's draw in a side to make this a right angled triangle. Label this side x.
STEP 5: Now we can think about what would happen if the radius travelled the entire way around the circle. The radius would travel a distance of . This is because the circumference of the circle is .
That's our key conversion:
This uses exactly the same trigonometric methods as we would when using degrees. You can adjust a calculator to display answers in radians:
Option -> Angle Unit -> Radians
Find the value of angle CAB, give your answer in radians.
Standard trigonometry question, figure out which of SOHCAHTOA we're using.
We have opposite and adjacent so TOA.
So we have to just perform an inverse trigonometric function so
Remember to make sure your calculator is in radians before performing this last step.
So Angle CAB has a size of .
Let's look at another example like this.
Find the value of .
We can use the sine rule here therefore
Make sure your calculator is correctly set in radians. This means that:
We have seen how the calculator can be converted into radians form. Now let's look at how we can convert directly between radians and degrees.
There is a key conversion:
And vice versa:
Let's see this in action.
Covert into radians.
And let's look at an example in the reverse direction.
Covert to degrees.
In the table below we can see some standard conversions between degrees and radians:
Radians are an angle unit like degrees but with a small conversion.
Remember that π radians = 180 °.
Remember to set the angle unit to radians on your calculator. This will simplify the answers to problems.
A radian is an angle unit like degrees, to help simplify solving trigonometric equations.
There are 2π radians in a circle.
Simplify divide by 180, then multiply your answer by π.
Be perfectly prepared on time with an individual plan.
Test your knowledge with gamified quizzes.
Create and find flashcards in record time.
Create beautiful notes faster than ever before.
Have all your study materials in one place.
Upload unlimited documents and save them online.
Identify your study strength and weaknesses.
Set individual study goals and earn points reaching them.
Stop procrastinating with our study reminders.
Earn points, unlock badges and level up while studying.
Create flashcards in notes completely automatically.
Create the most beautiful study materials using our templates.
Sign up to highlight and take notes. It’s 100% free.