Angles in standard Position

Slides:

Advertisements

Similar presentations

Warm Up Find the measure of the supplement for each given angle °2. 120° °4. 95° 30°60° 45° 85°

Advertisements

5.1 Angles and Degree Measures. Definitions An angle is formed by rotating one of two rays that share a fixed endpoint know as the vertex. The initial.

Angles and Their Measure Section Angles Vertex Initial Side Terminal Side.

6.3 Angles & Radian Measure

4-1.  Thinking about angles differently:  Rotating a ray to create an angle  Initial side - where we start  Terminal side - where we stop.

Angles in Degree & Radian Measure w/Unit Circle

Trigonometry The science of studying angle measure.

Radian Measure That was easy

Unit 7: Angles and Angle Measures

13-2 ANGLES AND THE UNIT CIRCLE FIND ANGLES IN STANDARD POSITION BY USING COORDINATES OF POINTS ON THE UNIT CIRCLE.

Warm Up List all multiples of 30° angles from 0° to 360 ° on Circle #1. List all multiples of 45 ° angles from 0° to 360 ° on Circle # 2. 30°, 60°, 90°,

6.1 Radian and Degree Measure

Warm Up Find the measure of the supplement for each given angle.

Section 4.1A Trigonometry (Degrees and Radians)

Aim: How do we look at angles as rotation?

Grade Homework HW 13.2A Answers.

Radian and Degree Measure

MATH 1330 Section 4.3.

ANGLE MEASURES PREACALCULUS LESSON 2 – 1.

Quadrants: Quarters on a coordinate plane

6.1 Radian and Degree Measure

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Coterminal Angles.

Radian and Degree Measure

6.1 Radian and Degree Measure

In The Coordinate Plane

10-2 Angles of Rotation Warm Up Lesson Presentation Lesson Quiz

Radian Measure and Coterminal Angles

What is a Radian? Before we begin our investigation of a radian let us first establish a definition of an angle and review some important concepts from.

Terms to know going forward

Unit 4, Day 1 Circular Trig.

Warm Up How’d the test go? Better? Worse?

Trigonometric Definitions

4.1 Radian and Degree measure

17-1 Angles of Rotation and Radian Measure

Radian and Degree Measure

Warm Up Find the inverse in expanded form: f x =−4+

Radian and Degree Measure

Warm Up Give radian measure for each: 90º b) 120º c) 135º

Warmup Find sin , cos , and tan .

Lesson 5-1: Angles and Degree Measure

6.1 Radian and Degree Measure

Angles and Angle Measure

Angles and Their Measures

Trigonometry Extended: The Circular Functions

Warmup: Which quadrant is indicated by “20° clockwise”?

Warm Up Give radian measure for each: 90º b) 120º c) 135º

Section T1- Angles and Their Measure

Angles and Radian Measure

Trigonometry Terms Radian and Degree Measure

Define General Angles and Radian Measure

Objectives Students will learn how to: Describe angles

Unit 5 Angles and Radian Measure

13.2A General Angles Alg. II.

Unit 7B Review.

MATH 1330 Section 4.3.

Welcome to Trigonometry!

Angles and Their Measure

Warm-up: Determine the circumference of the following circles in terms of π. HW: p (5 – 10 , , 25, 27, 33 – 36 , 43 – 61 odd, 71, 73)

Reference and Coterminal Angles

Warm Up Give radian measure for each: 90º b) 120º c) 135º

4.1 Radian and Degree measure

Mrs. Volynskaya Pre-Calculus 4.1 Radian and Degree Measure

Definition y Radian: The length of the arc above the angle divided by the radius of the circle. x in radians ,

Radian and Degree Measure

Warm Up Give radian measure for each: 90º b) 120º c) 135º

9.2 Angle and Radian Measure

13-2 Angles and Angle Measure

Warm Up Sketch one cycle of the sine curve:

Warm Up Sketch one cycle of the sine curve:

Presentation transcript:

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

B.y.o.d Warm-up 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?

What is an angle? It is composed of 2 rays:

Standard position 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

Examples of angles in standard position

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

You try. Draw the following angles in standard position: 45º 225º -540º

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

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

Next up Discovering Radians Activity

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

This leads to…. 360º, 2π

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

You try. Convert 60ºdegree to radians and then place on your circle. π/3 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

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

Exit Ticket---Now, use all of the info to sketch the following angles in standard position. 11π/6 5π/4 -π/2 4π -2π/3 5π/2 Homework: p. 105: 11-22