Alg2 Notes 10.3A and review.notebook
10­3A Converting Angles & Radians 10.3A: Convert from angles to radians and back
Arc length formula uses radians.
May 29, 2013
Alg2 Notes 10.3A and review.notebook
May 29, 2013
Alg2 Notes 10.3A and review.notebook
May 29, 2013
I. Definition of a Radian
A radian is a unit of angle measure based on arc length. If a central angle θ in a circle of radius r intercepts an arc of length r, then the measure of θ is defined as 1 radian.
Let's derive the conversions:
1. What is the length of the total circle?
2. What angle represents an entire rotation?
II. Converting Angles 1. Convert 30o to radians
2. Convert π/4 to degrees
Let's verify graphically
Alg2 Notes 10.3A and review.notebook
3. ­60o
May 29, 2013
4.
III. Coterminal Angles 5. Find the measure of an angle that is coterminal with each given angle:
a. b.
Alg2 Notes 10.3A and review.notebook
May 29, 2013
IV. Trig Functions of Radians & Degrees
6. Find the six trigonometric functions for the following angle measurements:
a. 330o
b. π 7. Find the six trigonometric functions for the following angle measurements:
a. ­270o
b. 5π/4 Alg2 Notes 10.3A and review.notebook
V. Arc Length 8. An minute hand on Big Ben’s Clock Tower in London is 14 ft long. To the nearest tenth of a foot, how far does the tip of the minute hand travel in 1 minute?
Step 1 Find the radius of the clock. r =14
Step 2 Find the angle θ through which the hour hand rotates in 1 minute.
Step 3 Find the length of the arc intercepted by radians.
The minute hand travels about 1.5 feet in one minute. May 29, 2013
Alg2 Notes 10.3A and review.notebook
May 29, 2013
10.3 p.711 #3 ­ 12(x3), 14, 16, 18, 21 ­ 33(x3), 36 ­ 39, 45, 51 ­ 55
Plan for the next few days...
Friday: Review Ch. 10.1­10.3 w/ Mr. Anderson
Monday: Group Quiz Ch. 10.1­10.3 w/ Mr. Anderson
Wednesday: Review for Final Day 1 w/ Ms. Best
Friday: Review for Final Day 2 w/ Ms. Best
Mon/Tu/Wed: Final Exam
Absolutely NO make­up work (corresponding to an excused absence) will be looked at during finals.