1. ## Radian Measure

5 a. Determine the measure of the central angle that is formed by an arc length of 5 cm in a circle with a radius of 2.5cm. Express the measure in both radians and degrees correct to one decimal place.

5cm

that's all i can think of i dont really know how to approach this problem i was away for a couple of days from school.

2. Originally Posted by Skoz
5 a. Determine the measure of the central angle that is formed by an arc length of 5 cm in a circle with a radius of 2.5cm. Express the measure in both radians and degrees correct to one decimal place.

$\displaystyle \frac{5}{2.5}$ so 2 radians?
That is exactly right.

3. Think of arc-length as part-way around a circle. If you go 20% of the way around a circle, you've gone 20% of the diameter. You've also subtended 20% of the 360 degrees in the circle.

Your circle has a circumference of $\displaystyle C=2{\pi}*r=2{\pi}*2.5=5{\pi}$

Remember percents are always calculated using $\displaystyle {{part}/{whole}}$ (times 100). If you've gone 5 cm around the circle, then you've gone $\displaystyle {5}/{5\pi}=1/{\pi}$ of the circle, or $\displaystyle {1}/{\pi}$ of 360 degrees, or $\displaystyle {1}/{\pi}$ of $\displaystyle 2{\pi}$ radians.

Half of the way around would be $\displaystyle 2{\pi}*1/2$ radians and one-fifth of the way around would be $\displaystyle 2{\pi}*1/5$ radians. For $\displaystyle {1}/{\pi}$ of the way around, the answer is $\displaystyle 2{\pi}*{1}/{\pi}=2$radians.