We are asked to describe what one degree and one radian represent. We know that one complete rotation of a circle equals 360 ^(∘).
Therefore, one degree represents an angle measure that equals 1360 of a rotation around a circle. On the other hand, one radian is defined as the measure of an angle in standard position that intercepts an arc of length r.
Let's now recall that the circumference of a circle is 2 π r. Therefore, one complete rotation of a circle is also equal to 2 π radians. This means that 360 ^(∘) and 2 π radians represent the same measure.
360 ^(∘) = 2 π ⟺ 180 ^(∘)= π
By using this equation, we can create our conversion factors to convert degrees to radians or radians to degrees.
Degrees to Radians: π/180 ^(∘)
Radians to Degrees: 180 ^(∘)/π
To convert degrees to radians we can multiply the number of degrees by π 180 ^(∘), and to convert radians to degrees we can multiply the number of radians by 180 ^(∘) π. Note that each of these ratios has a value of 1 since the numerator and denominator of each are equal.
