Alg2 Notes 10.3A and review.notebook

Alg2 Notes 10.3A and review.notebook May 29, 2013

103A Converting Angles & Radians

10.3A: Convert from angles to radians and back

Arc length formula uses radians.


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


4.3. 60o

III. Coterminal Angles

5. Find the measure of an angle that is coterminal with each given angle:

a. b.


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


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.

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.

r =14


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. AndersonMonday: Group Quiz Ch. 10.110.3 w/ Mr. AndersonWednesday: Review for Final Day 1 w/ Ms. BestFriday: Review for Final Day 2 w/ Ms. BestMon/Tu/Wed: Final Exam

Absolutely NO makeup work (corresponding to an excused absence) will be looked at during finals.

Alg2 Notes 10.3A and review.notebook

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