Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
3.1 Angles in the Coordinate Plane Trigonometry comes from the Greek words trigonon (triangle) and metron (measure). Two fundamental concepts needed for the study of trigonometry are angle and angle measure. In trigonometry, an angle is formed by rotating a ray about its endpoint. The initial side of the angle is the starting position of the ray and the terminal side is its ending position. y II I terminal side x vertex initial side III IV An angle in standard position has its initial side on the positive x-axis and its vertex at the origin. The measure of an angle describes the amount of rotation required to get from the initial side to the terminal side. If the rotation is counterclockwise, the angle has positive measure. If the rotation is clockwise, the angle has negative measure. An angle can be measured in degrees or in radians. An angle generated by one complete counterclockwise rotation measures 360 or 2 radians. y 360 x An angle generated by one complete clockwise rotation measures -360 or -2 radians. y -360 x Advanced Mathematics/Trigonometry: 3.1 Angles in a Coordinate Plane Page 1 Example 1: Find the degree measure of the angle for each given rotation and draw the angle in standard position. a. 3 rotation, counterclockwise 4 y x b. 1 rotation, clockwise 2 y x c. 2 1 rotation, counterclockwise 3 y x Advanced Mathematics/Trigonometry: 3.1 Angles in a Coordinate Plane Page 2 d. 7 rotation, clockwise 6 y x e. 2 rotation, clockwise 3 y x f. 11 rotation, counterclockwise 6 y x Advanced Mathematics/Trigonometry: 3.1 Angles in a Coordinate Plane Page 3 Example 2: The earth completes one rotation on its axis every 24 hours. Through how many degrees does a point on earth rotate in: a. 8 hrs b. 7 days c. 12 hrs d. 5 days e. 18 hrs f. 11 days The hour hand on a clock makes one rotation in 12 hours. Through how many degrees does the hour hand rotate in: g. 9 hrs h. 18 hrs Degrees may be divided into smaller parts by using decimals or by using minutes and seconds. Each degree is divided into 60 minutes (′) and each minute is divided into 60 seconds (″). Example 3: Express: a. 3650′10″ in decimal degrees b. 4040′5″ in decimal degrees c. 50.525 in degrees-minutes-seconds d. 15.345 in degrees-minutes-seconds Advanced Mathematics/Trigonometry: 3.1 Angles in a Coordinate Plane Page 4 Coterminal angles are angles of different measures with the same terminal side in standard position. If is the degree measure of an angle, then all angles coterminal with this angle have measure + 360k, where k is an integer. Example 4: Identify all coterminal angles with the given angle whose measures are between 0 and 360. a. -45 b. -200 c. -450 d. -750 e. -2100 Homework: p 123 => Class Exercises 1 – 8 (day 1) pp. 123-124 => Practice Exercises 1 – 10; 14 – 23 (day 2) Advanced Mathematics/Trigonometry: 3.1 Angles in a Coordinate Plane Page 5