Radians and Degrees

Definition of one radian

The measure of a central angle that intercepts an arc equal in length to the radius of the circle.

Formula to convert an angle from degrees ($D$) to radians ($R$)

$$R = D \times \frac{\text{π}}{180^\text{o}}$$

Formula to convert an angle from radians ($R$) to degrees ($D$)

$$D = R \times \frac{180^\text{o}}{\text{π}}$$

Exact radian equivalent of $270^\text{o}$

$$\frac{3\text{π}}{2}$$

Formula for arc length ($s$) of a circle given radius ($r$) and central angle ($\text{θ}$) in radians

$$s = r \text{θ}$$

Formula for the area of a circular sector ($A$) given radius ($r$) and central angle ($\text{θ}$) in radians

$$A = \frac{1}{2} r^2 \text{θ}$$

Exact degree equivalent of $\frac{5\text{π}}{6}\text{ radians}$

$$150^\text{o}$$

Exact radian equivalent of $315^\text{o}$

$$\frac{7\text{π}}{4}$$