Math - 2019-20
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.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
· 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.