Trigonometry2D

Angles and their Measure - Theory & Concepts - Trigonometry Arc Length Sector Area

Comprehensive guide to Degrees, Radians, Coterminal Angles, Arc Length, Sector Area, and Circular Segments with interactive visualizations.

Adjust the radius and angle to see how they govern the arc length ($s = r\theta$) and the sector area ($A = \frac12r^2\theta$).

Radius (

r

)3.0 units

1.02.03.04.05.0

Angle (

\theta

)120° / 2.094 rad

0°90°180°270°360°

1. Convert Angle to Radians:

\theta = 120^\circ \times \frac{\pi}{180^\circ} = 2.0944 \text{ rad}

2. Arc Length (

s = r\theta

s = 3.0 \times 2.0944

s = 6.2832 \text{ units}

3. Sector Area (

A = \frac{1}{2}r^2\theta

A = \frac{1}{2} \times (3.0)^2 \times 2.0944

A = 9.4248 \text{ units}^2

Note that

\theta

must be in radians when using these formulas. In degrees, the equivalents are

s = \frac{\theta}{360} \cdot 2\pi r

and

A = \frac{\theta}{360} \cdot \pi r^2

Sector Stats

s = 6.28A = 9.42

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