Radians

Japanese school year: Math II

What you learn

Learn how angles are measured in radians by dividing arc length by the radius, and convert between radians and degrees. Radians simplify mathematical calculations and are essential for calculus and physics modeling. Prior knowledge of circumference and sector formulas will help you transition smoothly to this topic.

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Key points

Formula to find the arc length $l$ of a circular sector with radius $r$ and central angle $\theta$ in radians. Measuring in radians lets you calculate $l$ simply by multiplying $r$ by $\theta$ .

l = r\theta

Formula to calculate the area $S$ of a sector with radius $r$ and central angle $\theta$ in radians. If arc length $l$ is known, it can be computed as $\frac{1}{2}lr$ .

S = \frac{1}{2}r^2\theta = \frac{1}{2}lr

This is the standard conversion rule between degrees and radians, stating that $180^\circ$ equals $\pi$ radians.

180^\circ = \pi

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Practice 1Coming soon