1 Section T1- Angles and Their Measure In this section, we will study the following topics: Terminology used to describe angles Degree measure of an angle Radian measure of an angle Converting between radian and degree measure

2 Angles Trigonometry translated: _____________ of _____________ Angle Measure

3 Standard Position Vertex at origin The initial side of an angle in standard position is always located on the positive x-axis.

Angle describes the amount and direction of rotation 120°–210° Positive Angle- rotates counter-clockwise (CCW) Negative Angle- rotates clockwise (CW)

5 Positive and negative angles When sketching angles, always use an arrow to show direction.

6 1. Sketch in standard position. In which quadrant is  located? 2. Sketch in standard position. In which quadrant is  located? Sketching Angles (Degrees)

Coterminal Angles Coterminal Angles-Two angles with the same initial and terminal sides (Hint: +360 and -360!!) Find 2 coterminal angles that correspond to the given angle. Ex1) 55 º Ex2) -112 º Ex3) 570 º Ex4) -420 º 7

8 Measuring Angles The measure of an angle is determined by the amount of rotation from the initial side to the terminal side. There are two common ways to measure angles, in degrees and in radians. ****************************************************************** We’ll start with degrees, denoted by the symbol º. One degree (1º) is equivalent to a rotation of of one revolution.

9 Acute and Obtuse Angles Acute angles have measure between _____º and _____º. Obtuse angles have measure between ____º and _____º. Straight angles measure _______º.

10 Angles are often classified according to the QUADRANT in which their terminal sides lie. Example: 50º is a ____ quadrant angle. 208º is a ____ quadrant angle. II I -75º is a _____ quadrant angle. III IV Classifying Angles

11 Classifying Angles Standard position angles that have their terminal side on one of the axes are called QUADRANTAL ANGLES. For example, 0º, 90º, 180º, 270º, 360º, … are quadrantal angles.

12 Complementary and Supplementary Angles Complementary Angles Def=Two positive angles whose sum is ______º Angles that measure 22º and ____º are complements. Supplementary Angles Def=Two positive angles whose sum is _______º Angles that measure 137º and ____º are supplements. EX) State the complement and supplement to each given angle. Ex1) Ex2)

13 In general, for  in radians, A second way to measure angles is in radians. Radian Measure Definition of Radian: One radian is the measure of a central angle  that intercepts arc s equal in length to the radius r of the circle.

14 Radian Measure

15 Radian Measure

16 Conversions Between Degrees and Radians 1. To convert degrees to radians, multiply degrees by 2. To convert radians to degrees, multiply radians by ***We are going to set up a conversion chart!!! Example Convert from Degrees to Radians: 210º

17 Conversions Between Degrees and Radians Example a) Convert from radians to degrees: b) Convert from radians to degrees:

18 Conversions Between Degrees and Radians Try it! c) Convert from degrees to radians (exact): d) Convert from radians to degrees:

19 Conversions Between Degrees and Radians Again! e) Convert from degrees to radians ( leave π in your answer! ): f) Convert from radians to degrees ( to nearest tenth ):

A Sense of Angle Sizes See if you can guess the size of these angles first in degrees and then in radians. You will be working so much with these angles, you should know them in both degrees and radians.

21 1. Sketch in standard position. In which quadrant is  located? 2. Sketch in standard position. In which quadrant is  located? Sketching Angles (Radians)