Using degree formula with radians or vice versa H
"The Radian Wrangle"
The Mistake in Action
Find the arc length where radius = 4 cm and angle = $\frac{\pi}{3}$ radians.
Wrong: Arc = $\frac{\pi/3}{360} \times 2\pi \times 4 = \frac{\pi}{540} \times 8\pi = \frac{8\pi^2}{540}$ cm
Why It Happens
Students use the degree formula ($\frac{\theta}{360} \times 2\pi r$) when the angle is given in radians.
The Fix
When using radians, the formulas simplify:
Arc length = $r\theta$ Sector area = $\frac{1}{2}r^2\theta$
For $r = 4$ and $\theta = \frac{\pi}{3}$:
Arc length = $4 \times \frac{\pi}{3} = \frac{4\pi}{3} = 4.19$ cm
Key: If the angle contains $\pi$ or is described as "radians", use the radian formulas!
Spot the Mistake
Can you identify where this student went wrong?
Angle = $\frac{\pi}{3}$ radians
Arc = $\frac{\pi/3}{360} \times 2\pi \times 4$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: