Today we will draw angles in standard position

Today we will draw angles in standard position and determine angles that are co-terminal.

§ Get out a piece of paper for today’s notes. § Please title the notes: “Angles in Standard Position” § Using your electronic device, please answer the following questions? Draw any graphs that support your explanations. § What is an angle? § What does it mean for an angle to be in standard position? § What is an initial ray and a terminal ray?

§ It is composed of 2 rays:

§ An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis (called the initial ray). § Important note: § Positive angles rotate counterclockwise § Negative angles rotate clockwise

§These angles terminate on an axis: Example: Which helps us establish this graph , 360º

§ Draw the following angles in standard position: § 45º § 225º §-540º

Angles that share the same initial side and terminal sides. To generate coterminal angles, it is as simple as adding or subtracting 360º

§Give three angles that are co-terminal with 150º. §Sample answers: -210º; 510º, 870º

§Discovering Radians Activity

§ As established in the “Discovering Radians Activity, ” 2π = 360º. Use this information to convert the following degree measurements to radians: § 90º § 180º § 270º

360º, 2π

§ Convert 45ºdegree to radians and then place on your circle: § Which then helps you establish radians in other quadrants 3π/4 360º, 2π 5π/4 7π/4

2π/3 § Convert 60ºdegree to radians and then place on your circle. § Now place the other measurements in the remaining quadrants. 360º, 2π 4π/3 5π/3

§ Convert 30ºdegree to radians and then place on your circle. § Now place the other measurements in the remaining quadrants. 5π/6 360º, 2π 7π/6 11π/6

§ 11π/6 § 5π/4 § -π/2 § 4π § -2π/3 § 5π/2 Homework: p. 105: 11 -22