Radians and arc length

The  exercise appears under the Trigonometry Math Mission. This exercise develops the idea of radian measure and the arc length formula.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the fraction of the circumference: This problem has a diagram of a circle with an arc length. The student is expected to find the fraction of the circle that is being highlighted.Raal1.png
 * 2) Write the formula for the arc length: This problem has a diagram of a circle and some variables as labels. The student is expected to use the variables to write the formula for the arc length.Raal2.png
 * 3) Find the measure of the angle: This problem has a diagram that has information about the arc length and the circumference of the circle. The student is expected to use this information to find the measure of the angle in radians.Raal3.png

Strategies
Knowledge of trigonometry and geometry in right triangles are encouraged to ensure success on this exercise.
 * 1) In radian mode, the arc length is given by $$s=r\theta $$.
 * 2) It is important to look closely to see which arc is being referred to.
 * 3) Ratios can also be used to find the desired values.

Real-life Applications

 * 1) Arc length is used in distinguishing between angular and linear velocities.
 * 2) Some forces in physics, such as centripedal and centrifrugal motion, use arc length in their derivation.
 * 3) In calculus the arc length formula is used in integral applications in polar coordinates.