Pre-Calc arc length notes

Pre-Calc tues 10/14
1. Calculate the area and arc length of a
2. Use arc length to estimate the size of
distant objects.
Problem solving
 We used a problem solving strategy to lead us to the
idea of apparent size, and knowledge of when we
might use it.
Problem solving from
the beginning
What question do you want to answer?
What do you need to answer it?
Answer the question.
Does you answer make sense?
Arc length
 The arc length of a sector, s, is given by the formula
 𝑠 = 𝑟𝜃, when theta is given in radians.
𝑠 =
∗ 2𝜋𝑟, when theta is given in degrees
Area of a sector
 The area of a sector, K, is:
 𝐾 = 𝑟 2 𝜃, when theta is given in radians
𝐾 =
∗ 𝜋𝑟 2 , when theta is in degrees
Apparent size
 The apparent size is the angle an object subtends
with your eye, when viewed from a distance.
 The height or diameter of an object can be estimated
using arc length, with apparent size as the central
angle of the sector.
 Distance from the observer to the object is the radius
of the sector.
 For small central angles the approximation is quite
For more information
 Talk to your peers who were in class.
 See your text book: read section 7-2, pg 263
 We did the class exercises in class.
 Pg. 265, written exercises 1-21 odd, plus #16