Objectives Convert angle measures between degrees and radians.

Slides:

Advertisements

Similar presentations

13-3 The Unit Circle Warm Up Lesson Presentation Lesson Quiz

Advertisements

13-3 The Unit Circle Warm Up Lesson Presentation Lesson Quiz

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

Objective: Convert between degrees and radians. Draw angles in standard form. Warm up Fill in the blanks. An angle is formed by two_____________ that have.

Warm-Up Exercises Simplify the expression. ANSWER 1 8 3π3π (9π)

Chapter 6: Trigonometry 6.3: Angles and Radian Measure

Introduction A sector is the portion of a circle bounded by two radii and their intercepted arc. Previously, we thought of arc length as a fraction of.

EXAMPLE 1 Use the formula for circumference Find the indicated measures. Write circumference formula. Substitute 9 for r. Simplify. Use a calculator. =

3.2 Angle Measures in Degrees & Radians. Another way to measure angles is in radians. 360  = 2π rad.  180  = π rad. –To convert from degrees to radians:

I can use both Radians and Degrees to Measure Angles.

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

Introduction All circles are similar; thus, so are the arcs intercepting congruent angles in circles. A central angle is an angle with its vertex at the.

13.3 – Radian Measures. Radian Measure Find the circumference of a circle with the given radius or diameter. Round your answer to the nearest tenth. 1.radius.

Converting between Degrees and Radians: Radian: the measure of an angle that, when drawn as a central angle of a circle, would intercept an arc whose.

EXAMPLE 1 Use the formula for circumference Find the indicated measures. Write circumference formula. Substitute 9 for r. Simplify. Use a calculator. =

Degrees, Minutes, Seconds

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

Arc Lengths, Sectors, and Rotational Speeds Dr. Shildneck Fall, 2014.

13-3 The Unit Circle Warm Up Lesson Presentation Lesson Quiz

Q1 of 36 Solve for x. Round to the nearest hundredths.  20 x 16.

EQ: How do you find an arc length and an area of a circular sector?

11.4 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Circumference and Arc Length.

Use the formula for circumference

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.

Warm Up Find the exact value of each trigonometric function. 1. sin 60°2. tan 45° 3. cos 45° 4. cos 60° 1 EQ: How can I convert between degrees and radians?

How do we convert angle measures between degrees and radians?

How do we convert angle measures between degrees and radians?

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

An angle whose vertex is at the center of the circle is called a central angle. The radian measure of any central angle of a circle is the length of the.

EXAMPLE 1 Use the formula for circumference Find the indicated measures. Write circumference formula. Substitute 9 for r. Simplify. Use a calculator.

Holt McDougal Algebra The Unit Circle 10-3 The Unit Circle Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson.

Topic 11-2 Radian Measure. Definition of a Radian Radian is the measure of the arc of a unit circle. Unit circle is a circle with a radius of 1.

Entry Task Radian measure I can… change Degrees to Radians and radians to degrees change Degrees to Radians and radians to degrees Find the measure.

13-3 The Unit Circle Warm Up Lesson Presentation Lesson Quiz

A little more practice You’ve got this! High five!

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

Radian and Degree Measure (part 2)

Aim: How do we define radians and develop the formula

Notes 6-1: Radian Measure

Introduction All circles are similar; thus, so are the arcs intercepting congruent angles in circles. A central angle is an angle with its vertex at the.

Examples Radians & Degrees (part 2)

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

Copyright © 2017, 2013, 2009 Pearson Education, Inc.

Chapter 4 Trigonometric Functions

6.1 Radian and Degree Measure

Introduction All circles are similar; thus, so are the arcs intercepting congruent angles in circles. A central angle is an angle with its vertex at the.

16.2 Arc Length and Radian Measure

Measuring Angles in Radians

Back to Trig Quick Review: Convert 200 degrees to radians

Section 4.1: Angles and Their Measures

Angles and Their Measures

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

Section 11.4 Circumference and Arc Length Theorem

11.1 Arc Length.

Degrees and radians.

Measuring Angles in Radians

Notes 4.1 – Angles and Their Measure

How do we convert angle measures between degrees and radians?

Warm Up a)Find the measure of the reference angle for each given angle. b) Find a pair of positive and negative coterminal angles for each given value.

Central Angles & Their Measures

Degrees and radians Unit 4.2.

Measuring Angles in Radians

11.1: Circumference and Arc Length

Angles and Their Measure

13-3 – Radian Measures.

9.2 Angle and Radian Measure

Unit 4: Circles and Volume

Adapted from Walch Education

Presentation transcript:

Objectives Convert angle measures between degrees and radians.

So far, you have measured angles in degrees So far, you have measured angles in degrees. You can also measure angles in radians. A radian is a unit of angle measure based on arc length. Recall from geometry that an arc is an unbroken part of a circle. If a central angle θ in a circle of radius r, then the measure of θ is defined as 1 radian.

The circumference of a circle of radius r is 2r The circumference of a circle of radius r is 2r. Therefore, an angle representing one complete clockwise rotation measures 2 radians. You can use the fact that 2 radians is equivalent to 360° to convert between radians and degrees.

Example 1: Converting Between Degrees and Radians Convert each measure from degrees to radians or from radians to degrees. A. – 60° . B.

Example 2 Convert each measure from degrees to radians or from radians to degrees. a. 80° 4 9 . b. 20 .

Example 3: Automobile Application A tire of a car makes 653 complete rotations in 1 min. The diameter of the tire is 0.65 m. To the nearest meter, how far does the car travel in 1 s? Step 1 Find the radius of the tire. The radius is of the diameter. Step 2 Find the angle θ through which the tire rotates in 1 second. Write a proportion.

Example 3 Continued The tire rotates θ radians in 1 s and 653(2) radians in 60 s. Cross multiply. Divide both sides by 60. Simplify.

Example 3 Continued Step 3 Find the length of the arc intercepted by radians. Use the arc length formula. Substitute 0.325 for r and for θ Simplify by using a calculator. The car travels about 22 meters in second.

Example 4 A minute hand on Big Ben’s Clock Tower in London is 14 ft long. To the nearest tenth of a foot, how far does the tip of the minute hand travel in 1 minute? Step 1 Find the radius of the clock. r =14 The radius is the actual length of the hour hand. Step 2 Find the angle θ through which the hour hand rotates in 1 minute. Write a proportion.

Example 4 Continued The hand rotates θ radians in 1 m and 2 radians in 60 m. Cross multiply. Divide both sides by 60. Simplify.

Example 4 Continued Step 3 Find the length of the arc intercepted by radians. Use the arc length formula. Substitute 14 for r and for θ. s ≈ 1.5 feet Simplify by using a calculator. The minute hand travels about 1.5 feet in one minute.