Section 4.2 – Radians, Arc Length, and the Area of a Sector 4 Sector Area Formula In a circle of radius r, the area A of a sector with central angle of radian measure T is given by . For example, let's find the length of the arc when \(\theta\) = \( 150^{\circ} \) and \(radius = 36 \) inches So first let's see how we convert \( 150^{\circ} \) into radians. Arc Length in Radian DRAFT. When the central angle is in radians, the arc length formula is: Arc length … angle in degree to radians: multiply by $\pi$/180; arc length equation in degree to radians: multiply by 180/$\pi$). So in … with its equivalent "central angle", we can establish the formula: Notice that arc length is a fractional part of the circumference. Topical Outline | Geometry Outline | MathBitsNotebook.com | MathBits' Teacher Resources … Imagine some arc, and then extend each of the ends. Radian Arc-Length Formula Given a circle of radius = r and a central angle in radian, let L = length of the arc cuts off by the angle , then L = r An angle based at the center of a circle is called a central angle. The circumference itself can be considered a full circle arc length. Easy! The length of a circular arc depends on what two variables? For example, an arc measure of 60º is one-sixth of the circle (360º), so the length of that arc will be one-sixth of the circumference of the circle. If we solve the proportion for arc length, and replace "arc measure". 1.2 Radian Measure, Arc Length, and Area Find the arc length if we have a circle with a radius of 3 meters and central angle of 0.52 radian. The Trigonometry of Circles - Cool Math has free online cool math lessons, cool math games and fun math activities. Worksheet to calculate arc length and area of sector (radians). Worksheet to calculate arc length and area of sector (radians). To use the arc length calculator, simply enter the central angle and the radius into the top two boxes. All this means is that by the power of radians and proportions, the length of an arc is nothing more than the radius times the central angle! As you progress in your study of mathematics and angles, you will see more references made to the term "radians" instead of "degrees". Arc Length and Sector Area You can also find the area of a sector from its radius and its arc length. Arc length formula is used to calculate the measure of the distance along the curved line making up the arc (a segment of a circle). Find angle subten The length of an arc depends on the radius of a circle and the central angle θ.We know that for the angle equal to 360 degrees (2π), the arc length is equal to circumference.Hence, as the proportion between angle and arc length is constant, we can say that: Convert using the following facts. 3.5 Arc Length and Area Arc Length On a circle of radius 1 an arc of length s subtends an angle (the Greek letter theta) whose radian measure is numerically equal to s.That is, s = is the very definition of radian measure.