# *T.9 - Arcs, Sectors, Velocity

T.9  The student will solve problems, including practical problems, involving

a)  arc length and area of sectors in circles using radians and degrees;

b)  linear and angular velocity.

### UNDERSTANDING THE STANDARD

·  Degrees and radians are units of angle measure.

·  A radian is the measure of the central angle that is determined by an arc whose length is the same as the radius of the circle.

·  The relationship between the radian measure of an angle and the length of the intercepted arc can be represented by , where s is the arc length, r is the length of the radius, and  is the measure of the angle.

### ESSENTIALS

·  T.9a1  Convert between any angle expressed in radians and degrees without using a graphing utility.

·   T.9a2  Derive the relationship between the radian measure of an angle and the length of the intercepted arc.

·   T.9a3  Calculate the length of an arc in radians.

·   T.9a4  Calculate the area of sectors in circles.

·   T.9b1  Solve practical problems involving linear and angular velocity.

### KEY VOCABULARY

Updated: Oct 27, 2017