Convert Between Degrees and Radians - Pre-Calculus

In order to solve this problem, we need to know that

using this formula, we can find our answer:

In order to solve this problem, we need to know that

using this formula, we can find our answer:

In order to solve this problem, we need to know that

we can arrive to our answer by using this formula:

To solve this problem, we need to know that

we can arrive to our answer by using this formula:

To convert, multiply by the conversion factor .

The value of radians equal 180 degrees. Substitute and solve.

To convert from degrees into radians,

multiply the angle in degrees by

To convert between degrees and radians, you must use the following conversion factor 180 degrees = pi radians.

Therefore:

To convert from radians to degrees, multiply the input by .

In this case:

To convert from degrees to radians, multiply the input by:

In this case:

In order to convert from radians to degrees, we will need to know how many degrees are in a radian.

Substitute 180 as a replacement for .

The correct answer is .

To convert degrees to radians we must recall the conversion factor. Remember that .

Therefore, we can create the following fraction and solve for the missing variable.

Megan, a civil engineer, measures the angle made by the angle of a road. She finds the angle to be . What is the angle in radians?

To convert from degrees to radians, use the following formula:

Where and stand for degrees and radians, respectively.

So we get

While SCUBA diving as part of a search and rescue diving operation, Daniel is responsible for covering a sector which represents radians. What is this angle in degrees?

Recall the following formula for converting radians to degrees:

Where d and r are angle measures in degrees and radians, respectively.

So, we are given a value in radians and asked to find it in degrees. Plug in to the above formula to find the answer!

So our answer is:

Terry is running around a circular track. If he covers in 120 seconds, how many degrees has he covered?

To convert from radians to degrees, use the following helpful formula:

Where r and d are our desired angle measure in radians and degrees, respectively.

So, we have r, plug in and simplify to get d!

Making our answer:

To convert from degrees to radians, you do:

To solve, use the conversion factor . Thus,

To convert from degrees to radians, you must multiply by : . Then, multiply across as you do normally with fractions. Try and simplify if you can. In this case, 60 goes into both 660 and 180.

Thus, your answer is .

To convert from radians to degrees, you must multiply by so that you then get . Then, simplify and multiply straight across so that your answer is .