Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 6.1 Angles and Their Measure.

Slides:

Advertisements

Similar presentations

Sullivan Precalculus: Section 5.1 Angles and Their Measures

Advertisements

Section 5.1 Angles and Arcs Objectives of this Section Convert Between Degrees, Minutes, Seconds, and Decimal Forms for Angles Find the Arc Length of a.

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.

7.2 Radian Measure.

Copyright © 2003 Pearson Education, Inc. Slide Radian Measure, Arc Length, and Area Another way to measure angles is using what is called radians.

Degrees, Minutes, Seconds

6.1.2 Angles. Converting to degrees Angles in radian measure do not always convert to angles in degrees without decimals, we must convert the decimal.

Geometric Representation of Angles.  Angles Angles  Initial Side and Standard Position Initial Side and Standard Position.

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

Copyright © 2011 Pearson Education, Inc. Radian Measure, Arc Length, and Area Section 1.2 Angles and the Trigonometric Functions.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 7.1 Angles and Their Measure.

Trigonometry #3 Radian Measures. Converting Degrees to Radians Angle measure In degrees.

Can you draw a radius to each point of tangency? What do you notice about the radius in each picture?

Angles and Their Measure. 1. Draw each angle (Similar to p.105 #11-22)

Warm Up 1)Are the following functions periodic? 2) Write the equation of a cosine function given the following information: Amplitude = 5, Period = π,

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 6.1 Composite Functions.

Arc Length Start with the formula for radian measure … … and multiply both sides by r to get … Arc length = radius times angle measure in radians.

Copyright © 2011 Pearson, Inc. 4.1 Angles and Their Measures.

7.2 – Sectors of Circles Essential Question: How do you find the radius of a sector given its’ area and arc length?

Section 2.1 Angles and Their Measure. Sub-Units of the Degree: “Minutes” and “Seconds” (DMS Notation)

Copyright © 2011 Pearson, Inc. 4.1 Angles and Their Measures.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 7.1 Angles and Their Measure.

6.1 Angles and Radian Measure Objective: Change from radian to degree measure and vice versa. Find the length of an arc given the measure of the central.

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

1° = 60 ′ 1 ′ = 60 ″ Convert 50°6 ′ 21 ″ 50° + 6 × (1/60)° + 21 × (1/60) × (1/60)° = ° Convert to degrees 21° +.256(60 ′ ) 21° ′

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

10-7 Area of Circles and Sectors. REVIEW Circumference: The total distance (in length) around a circle. Arc measure: The measure of the central angle.

Pre-Calculus Honors Pre-Calculus 4.1: Radian and Degree Measure HW: p (14, 22, 32, 36, 42)

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 4-1) Then/Now New Vocabulary Example 1:Convert Between DMS and Decimal Degree Form Key Concept:Radian.

Section 7.1 Angles and Their Measure Copyright © 2013 Pearson Education, Inc. All rights reserved.

The Inverse Trigonometric Functions (Continued)

Warm-Up: If , find tan θ..

Angles and Their Measure

Angles and Their Measure

Section5.1 Angles and Their Measure

Section 9.1 Polar Coordinates

Section R.8 nth Roots; Rational Exponents

Chapter 4: Lesson 4.1 Radian & Degrees

1.2 Radian Measure, Arc Length, and Area

Angles and Their Measure

Angles and Their Measure

Convert degree measures of angles to radian measures, and vice versa.

Chapter 7 Section 1.

Warm Up Write an equation for a cosine function with the following characteristics. Amplitude: 4 Period:  Phase shift: left 3 Vertical shift: down 4.

Arc length and area of a sector.

Section 2.4 Circles Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Angles and Their Measure

Angles and Their Measure

Angles and Their Measure

Section 8.3 The Law of Cosines

Section 4.1: Angles and Their Measures

Section 11.8 Linear Programming

Copyright © 2008 Pearson Prentice Hall Inc.

Copyright © 2008 Pearson Prentice Hall Inc.

Warm-Up: If , find tan θ..

Mathematical Models: Building Functions

Copyright © 2008 Pearson Prentice Hall Inc.

Copyright © 2008 Pearson Prentice Hall Inc.

LESSON 4–2 Degrees and Radians.

Systems of Linear Equations: Matrices

Quadratic Equations in the Complex Number System

Properties of Rational Functions

Section 4.1 Angles and Their Measure

Angles and Their Measure

Angles and Their Measure

Copyright © 2008 Pearson Prentice Hall Inc.

Copyright © 2008 Pearson Prentice Hall Inc.

The Inverse Trigonometric Functions (Continued)

Angles and Their Measure

Presentation transcript:

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 6.1 Angles and Their Measure

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

(a)Convert 40°12 ’ 5 ” to a decimal in degrees. Round the answer to four decimal places. (b)Convert ° to the D°M ’ S ” form. Round the answer to the nearest second.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Radians

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Find the length of the arc of a circle of radius 4 meters subtended by a central angle of 0.5 radian.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

(a) 30° (b) 120° (c)  60° (d) 270° (e) 104 °

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Find the area of the sector of a circle of radius 5 feet formed by an angle of 60°. Round the answer to two decimal places.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Linear Speed Angular Speed

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. A child is spinning a rock at the end of a 3-foot rope at the rate of 160 revolutions per minute (rpm). Find the linear speed of the rock when it is released. 3