#### Math - 2018-19

# 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.

*Adopted: 2016*

### BIG IDEAS

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - T.9 Understanding

· 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

**The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to**

·
T.9a_{1}** Convert**
between any angle expressed in radians and degrees without using a graphing
utility.

· T.9a_{2}** Derive** the relationship
between the radian measure of an angle and the length of the intercepted arc.

· T.9a_{3}** Calculate** the length of an
arc in radians.

· T.9a_{4}** Calculate** the area of
sectors in circles.

· T.9b_{1}** Solve** practical problems
involving linear and angular velocity.

### KEY VOCABULARY

*Updated: May 29, 2018*