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

Slides:

Advertisements

Similar presentations

Angles of Rotation and Radian Measure In the last section, we looked at angles that were acute. In this section, we will look at angles of rotation whose.

Advertisements

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

Objectives: Be able to draw an angle in standard position and find the positive and negative rotations. Be able to convert degrees into radians and radians.

What Is A Radian? 1 radian = the arc length of the radius of the circle.

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

Radian and Degree Measure In this section, we will study the following topics: Terminology used to describe angles Degree measure of an angle Radian.

WARM UP 1. What do complementary angles add to? 2. What do supplementary angles add to? 3. Find a the complementary angle and supplementary angle to 60.

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

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.

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

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.

13.2 Angles and Angle Measure

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.

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.

Unit 1, Lesson 1 Angles and their Measures. What is an angle? Two rays with the same Endpoint.

Math III Accelerated Chapter 13 Trigonometric Ratios and Functions 1.

6.1: Angles and their measure January 5, Objectives Learn basic concepts about angles Apply degree measure to problems Apply radian measure to problems.

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

Trigonometric Functions

Trigonometry Day 1 ( Covers Topics in 4.1) 5 Notecards

AAT-A 4/25/14 Obj: SWBAT convert from degrees to radians and vice versa. Agenda Bell Ringer: Inquiry: Angle measure HW Requests: Comments on ACT Turn in.

4.1 Radian and Degree Measure I. Angles (2 rays: an Initial side & a Terminal side). A) Initial side = the starting ray of the angle. 1) It is on the +

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

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.

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.

13.2 Angles of Rotation and Radian Measure

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.

Section 4.1 Angles and Their Measures Trigonometry- measurement of angles IMPORTANT VOCABULARY: Angle- determined by rotating a ray about its endpoint.

Radian and Degree Measure. Radian Measure A radian is the measure of a central angle that intercepts an arc length equal to the radius of the circle Radians.

Table of Contents 1. Angles and their Measures. Angles and their Measures Essential question – What is the vocabulary we will need for trigonometry?

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

How do we draw angles in standard position?

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

Math Analysis Chapter Trig

An angle is formed by rotating an initial arm about a fixed point. Angles in Standard Position - Definitions An angle is said to be in standard position.

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.

Radian Angle Measures 1 radian = the angle needed for 1 radius of arc length on the circle still measures the amount of rotation from the initial side.

1.1 Trigonometry.

Aim: How do we look at angles as rotation? Do Now: Draw the following angles: a) 60  b) 150  c) 225  HW: p.361 # 4,6,12,14,16,18,20,22,24,33.

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.

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

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

MATH 1330 Section 4.3 Trigonometric Functions of Angles.

Agenda Notes : (no handout, no calculator) –Reference Angles –Unit Circle –Coterminal Angles Go over test Go over homework Homework.

Section 4.1. Radian and Degree Measure The angles in Quadrant I are between 0 and 90 degrees. The angles in Quadrant II are between 90 and 180 degrees.

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.

Table of Contents 1. Angles and their Measures. Angles and their Measures Essential question – What is the vocabulary we will need for trigonometry?

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

Table of Contents 2. Angles and their Measures - Radians.

Chapter 4 Part 1.  Def: A radian is the measure of an angle that cuts off an arc length equal to the radius.  Radians ↔ Degrees ◦ One full circle.

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

Table of Contents 1. Angles and their Measures. Angles and their Measures Essential question – What is the vocabulary we will need for trigonometry?

Quadrants: Quarters on a coordinate plane

Radian and Degree Measure

6.1 Radian and Degree Measure

Radian Measure and Coterminal Angles

17-1 Angles of Rotation and Radian Measure

6.1 Radian and Degree Measure

Radian and Degree Measure

Reference and Coterminal Angles

Mrs. Volynskaya Pre-Calculus 4.1 Radian and Degree Measure

Presentation transcript:

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

Trigonometry vocabulary Initial side – start side of angle Terminal side – end side of angle Standard position – An angle whose initial side is on the positive x-axis Coterminal angle – Angles that have the same terminal side Reference angle – The acute angle formed by the terminal side of the given angle and the x-axis. 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.

Positive angles Initial side on the positive x-axis and rotate counterclockwise

Negative angles Initial side on the positive x-axis and rotate clockwise

Quadrants Quadrant III Quadrant I Quadrant II Quadrant IV

Angles of the axes

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. The ray on the x-axis is called the initial side and the other ray is called the terminal side.

Examples What quadrant is the terminal side of the angle in? (Make a sketch of the angle)

Reference angles The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. Reference angles may appear in all four quadrants. Angles in quadrant I are their own reference angles.

Examples What are the reference angles for each of these angles?

Radians Angle degrees can also be expressed in radians Radians is the ratio of the length of an arc to its radius Radians are expressed in terms of = 180 o To change from degrees to radians, multiply by and reduce. To change from radians to degrees, multiply by

Examples Change from degrees to radians Change from radians to degrees

Examples - Coterminal angles You can add or subtract multiples of 360 or -360 to find coterminal angles Find 2 coterminal angles (one positive and one negative) for 35 o Find 2 coterminal angles (one positive and one negative) for -23 o Find 2 coterminal angles (one positive and one negative) for 740 o

Coterminal Examples using radians Add or subtract 2π to angle