12.2 – Angles and Angle Measure. Standard Position – when the vertex of the angle is at the origin and one ray is on the positive x-axis. Initial Side.

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

2.1 Angles and Their Measures

Chapter 6: Trigonometry 6.3: Angles and Radian Measure

Angles and Arcs in the Unit Circle Radian and Degree Measure In this section, we will study the following topics: Terminology used to describe.

Unit 4: Intro to Trigonometry. Trigonometry The study of triangles and the relationships between their sides and angles.

H.Melikian/12001 Recognize and use the vocabulary of angles. Use degree measure. Use radian measure. Convert between degrees and radians. Draw angles in.

Angles and Radian Measure Section 4.1. Objectives Estimate the radian measure of an angle shown in a picture. Find a point on the unit circle given one.

Sec 6.1 Angle Measure Objectives:

Angles and Radian Measure. 4.1 – Angles and Radian Measure An angle is formed by rotating a ray around its endpoint. The original position of the ray.

Section 4.1 Angles and Radian Measure. The Vocabulary of Angles An angle is formed by two rays that have a common endpoint. One ray is called the initial.

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

Copyright © Cengage Learning. All rights reserved. Trigonometric Functions: Right Triangle Approach.

4.1 Radian and Degree Measure. Objective To use degree and radian measure.

I can use both Radians and Degrees to Measure Angles.

Section 4.1.  Trigonometry: the measurement of angles  Standard Position: Angles whose initial side is on the positive x-axis 90 º terminal 180 º 0º.

Section 4.1 Radian and Degree Measure. We will begin our study of precalculus by focusing on the topic of trigonometry Literal meaning of trigonometry.

6.3 Angles & Radian Measure

13.2 Angles and Angle Measure

5.1 Angles and Radian Measure. ANGLES Ray – only one endpoint Angle – formed by two rays with a common endpoint Vertex – the common endpoint of an angle’s.

Radian and Degree Measure Objectives: Describe Angles Use Radian and Degree measures.

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

Lesson 7-1 Angles, Arcs, and Sectors. Objective:

Unit 6 Day 1 December 12 th copyright2009merrydavidson Sit on your paper plate! Take markers, ruler, 1 pipe cleaner and protractor. Do not bend the pipe.

Warm up for 8.5 Compare the ratios sin A and cos B Compare the ratios sec A and csc B Compare the ratios tan A and cot B pg 618.

7.1 – Measurement of Angles

Section 7.1 Angles and Their Measure. ANGLES An angle is formed by rotating a ray about its endpoint. The original ray is the initial side of the angle.

Advanced Algebra II Advanced Algebra II Notes 10.2 continued Angles and Their Measure.

Grade 12 Trigonometry Trig Definitions. Radian Measure Recall, in the trigonometry powerpoint, I said that Rad is Bad. We will finally learn what a Radian.

Math III Accelerated Chapter 13 Trigonometric Ratios and Functions 1.

A3 5.1a & b Starting the Unit Circle! a)HW: p EOO b)HW: p EOE.

Angles in Degree & Radian Measure w/Unit Circle

Trigonometry The science of studying angle measure.

Bell Ringer ( ) Using any available source define: 1. Radian 2. Standard Position 3. Coterminal 4. Intercepted Arc 5. Reference Angle 6. Unit Circle.

Concept. Example 1 Draw an Angle in Standard Position A. Draw an angle with a measure of 210° in standard position. 210° = 180° + 30° Draw the terminal.

13-3 Radian Measure Today’s Objective: I can measure an angle in radians.

Terms to know going forward Angle: 2 rays an initial side and a terminal side. Initial side Terminal side Positive angle goes counter clockwise. Negative.

Lesson Handout #1, 3, 9, (ODD), 27, 28, (ODD), (EOO)

Objectives Change from radian to degree measure, and vice versa Find angles that are co-terminal with a given angle Find the reference angle for a given.

Radians and Degrees. What the heck is a radian? The radian is a unit of angular measure defined such that an angle of one radian subtended from the center.

Chapter 4 Trigonometric Functions. Angles Trigonometry means measurement of triangles. In Trigonometry, an angle often represents a rotation about a point.

Find all 6 trig ratios from the given information sinθ = 8/133. cotθ = 5   9 15.

More Trig – Angles of Rotation Learning Objective: To find coterminal and reference angles and the trig function values of angles in standard position.

MATHPOWER TM 12, WESTERN EDITION Chapter 4 Trigonometric Functions 4.1.

Radian Measure That was easy

Radians and Angles. Angle-formed by rotating a ray about its endpoint (vertex) Initial Side Starting position Terminal Side Ending position Standard Position.

LESSON 6-1: ANGLES & THE UNIT CIRCLE BASIC GRAPHING OBJECTIVE: CONVERT BETWEEN DEGREE AND RADIAN MEASURE, PLACE ANGLES IN STANDARD POSITION & IDENTIFY.

Unit 7: Angles and Angle Measures

Chapter 4 Trigonometric Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Angles and Radian Measure.

Angle Measures in Degrees & Radians Trigonometry 1.0 Students understand the notation of angle and how to measure it, in both degrees and radians. They.

Ch 14 Trigonometry!!. Ch 14 Trigonometry!! 14.1 The unit circle Circumference Arc length Central angle In Geometry, our definition of an angle was the.

Vocabulary Origin & Quadrants Vertex Right, Acute, & Obtuse Complementary & Supplementary Central & Inscribed Angles Arc.

Angles and their Measures Essential question – What is the vocabulary we will need for trigonometry?

 Think back to geometry and write down everything you remember about angles.

Holt McDougal Algebra Angles of Rotation Warm Up Find the measure of the supplement for each given angle. Think back to Geometry… °2. 120°

Introduction to Trigonometry Angles and Radians (MA3A2): Define an understand angles measured in degrees and radians.

4.2 Degrees and Radians Objectives: Convert degree measures of angles to radian measures Use angle measures to solve real-world problems.

Trigonometry Section 7.1 Find measures of angles and coterminal angle in degrees and radians Trigonometry means “triangle measurement”. There are two types.

13.2 General Angles and Radian Measure. 1. I want the exact value (not the decimal value from the calculator) 1. I want the exact value (not the decimal.

Chapter 5 Trigonometric Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Angles and Radian Measure.

FST Section 4.1. Tate lives three miles from school. He decided to ride his bicycle to school one nice day. If the front wheel turned at an average speed.

Section 4.1.  A ray is a part of a line that has only one endpoint and extends forever in the opposite direction.  An angle is formed by two rays that.

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

Angles and Their Measure Section 4.1 Objectives I can label the unit circle for radian angles I can determine what quadrant an angle is in I can draw.

Part 1.  We interpret an angle as a rotation of the ray R 1 onto R 2.  An angle measure of 1 degree is formed by rotating the initial side th of a complete.

Algebra II Honors B Block Groups Iman Kristin Phillip Katy Phil T. Hunter Mike Paul John Becky Rachel Krista Claire.

Chapter 7: Trigonometric Functions Section 7.1: Measurement of Angles.

Math Angles Note 1 Definition: An angle is created when a half-ray (initial side) is rotated around a point (the vertex) and stops at a new.

Warmup Find sin , cos , and tan .

Angles and Angle Measure

Presentation transcript:

12.2 – Angles and Angle Measure

Standard Position – when the vertex of the angle is at the origin and one ray is on the positive x-axis. Initial Side – the ray on the x-axis. (where the angle starts.) Terminal Side - the ray that rotates about the center. (where the angle ends.)

Example 1: Draw an angle with the given measure in standard position. a. 210° b. –45°

Example 2: a. In a springboard diving competition, a diver made a 900-degree rotation before slicing into the water. Draw an angle in standard position that measures 900°.

Example 2: b. While riding down the mountain, a snowboarder goes off a jump and turns 600° before touching down onto the snow again. Determine how many degrees past the positive x-axis the snowboarder lands.

Coterminal Angles: - Two or more angles in standard position with the same terminal side. - How can we find coterminal angles???

Example 3: Find an angle with a positive measure and an angle with a negative measure that are coterminal with each angle. b. 210° b. –120°

Radians:

Example 4: Conversions a. Rewrite 30° in radians. b. Rewrite 120° in radians.

Example 5: Conversions

- Central Angle – an angle with a vertex at the center of the circle.

Example 6: a. The steering wheel on a monster truck has a radius of 11 inches. How far does a point on the steering wheel travel if the wheel makes four fifths of a rotation?

Example 6: b. The steering wheel on a yacht has a radius of 16 inches. How far does a point on the steering wheel travel if the wheel makes five sevenths of a rotation?