What is a radian? · A RADIAN is the measure of a central angle that intercepts an arc with the...

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Lesson 6.3 ~ Radian Measure Objectives: • I understand the definition of a radian. • I can convert between radian and degree measure. • I can find the sine and cosine of a radian measure. • I can find arc length in radian measure. • I can use radian measure to solve real world problems.

Transcript of What is a radian? · A RADIAN is the measure of a central angle that intercepts an arc with the...

Page 1: What is a radian? · A RADIAN is the measure of a central angle that intercepts an arc with the length equal to the radius of the circle. Radians measure the amount of rotation between

Lesson 6.3 ~ Radian Measure

Objectives:

• I understand the definition of a radian. • I can convert between radian and degree measure. • I can find the sine and cosine of a radian measure. • I can find arc length in radian measure. • I can use radian measure to solve real world problems.

Page 2: What is a radian? · A RADIAN is the measure of a central angle that intercepts an arc with the length equal to the radius of the circle. Radians measure the amount of rotation between

What is a radian?

Page 3: What is a radian? · A RADIAN is the measure of a central angle that intercepts an arc with the length equal to the radius of the circle. Radians measure the amount of rotation between
Page 4: What is a radian? · A RADIAN is the measure of a central angle that intercepts an arc with the length equal to the radius of the circle. Radians measure the amount of rotation between
Page 5: What is a radian? · A RADIAN is the measure of a central angle that intercepts an arc with the length equal to the radius of the circle. Radians measure the amount of rotation between

How do you remember which fraction to multiply by when converting between radians and degrees?  

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Must show conversion work – we’re practicing here!

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Remember how to find coterminal angles when our angles were in degrees?

How do you think we find coterminal angles when our angles are in radian?

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d

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1

0

Opposite

Adjacent

sin    =  cos    = 

tan    = 

0 0

0

What is tangent & how can we find it on the unit circle?

(Think SOH CAH TOA)

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How could you find the arc length on a circle?

8 in.

L

Page 13: What is a radian? · A RADIAN is the measure of a central angle that intercepts an arc with the length equal to the radius of the circle. Radians measure the amount of rotation between

Stop and think!  An angle in standard position on a unit circle can have a negative measure.  When calculating the length of an intercepted arc, we take the absolute value of the angle measure?  Why?

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three decimal places.

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three decimal places.

Page 16: What is a radian? · A RADIAN is the measure of a central angle that intercepts an arc with the length equal to the radius of the circle. Radians measure the amount of rotation between
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Assignment:Section 6.3:  problems 8­23, 25, 27, 28

(On #14­17, also state one positive and one negative coterminal angle.  On calculator problems, round to three decimals, not two.)

AND

Trigonometry Unit Circle Monster(Do the monster by memory.  This uses the unit circle we made, 

but you should have the pattern memorized by now.)


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

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

Radian Measure and Coterminal Angles

Radian Measure and Coterminal Angles

Introduction to Radian Measure

Introduction to Radian Measure

6.3Angles & Radian Measure

6.3Angles & Radian Measure

4.1 Radian and Degree Measure...Section 4.1 Radian and Degree Measure 287 Applications The radian measureformula, can be used to measure arc length along a circle. Finding Arc Length

4.1 Radian and Degree Measure...Section 4.1 Radian and Degree Measure 287 Applications The radian measureformula, can be used to measure arc length along a circle. Finding Arc Length

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.

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.

3.1 Radians Angles are measured in degrees. Angles may also be measured in radians One radian is the measure of the central angle of a circle that intercepts.

3.1 Radians Angles are measured in degrees. Angles may also be measured in radians One radian is the measure of the central angle of a circle that intercepts.

9.2 Define General Angles and Use Radian Measure What are angles in standard position? What is radian measure?

9.2 Define General Angles and Use Radian Measure What are angles in standard position? What is radian measure?

Radian and Degree Measure

Radian and Degree Measure

Radians Radian measure is an alternative to degrees and is based upon the ratio of arc length (al) radius r θ al θ- theta.

Radians Radian measure is an alternative to degrees and is based upon the ratio of arc length (al) radius r θ al θ- theta.

Radians, Arc Length and Sector Area. Radians Radians are units for measuring angles. They can be used instead of degrees. r O 1 radian is the size of.

Radians, Arc Length and Sector Area. Radians Radians are units for measuring angles. They can be used instead of degrees. r O 1 radian is the size of.

Chapter 4 Trigonometric Functions 1. 4.1 Radian & Degree Measure Objectives: Describe angles. Use radian measure. Use degree measure and convert.

Chapter 4 Trigonometric Functions 1. 4.1 Radian & Degree Measure Objectives: Describe angles. Use radian measure. Use degree measure and convert.

PreCal2 Review Test2 2016 · 2018. 3. 6. · PreCal2 Review Test2 2016 1. Express 10 /3 radians in degree measure. 2.Express 315º in radian measure. 3.Express 450º in radian measure.

PreCal2 Review Test2 2016 · 2018. 3. 6. · PreCal2 Review Test2 2016 1. Express 10 /3 radians in degree measure. 2.Express 315º in radian measure. 3.Express 450º in radian measure.

6.1 Radian and Degree Measure

6.1 Radian and Degree Measure

5.1 Angles and Radian Measure

5.1 Angles and Radian Measure

Sec 6.1 Angle Measure Objectives: To understand the difference between radian measure and degree measure. To convert between radians and degrees. To understand.

Sec 6.1 Angle Measure Objectives: To understand the difference between radian measure and degree measure. To convert between radians and degrees. To understand.

11X1 T08 01 radian measure (2010)

11X1 T08 01 radian measure (2010)

4.1: Radian and Degree Measure

4.1: Radian and Degree Measure

Slide 1-1 3 Radian Measure and the Unit Circle. Slide 1-2 3.1 Radian Measure 3.2 Applications of Radian Measure 3.3 The Unit Circle and Circular Functions.

Slide 1-1 3 Radian Measure and the Unit Circle. Slide 1-2 3.1 Radian Measure 3.2 Applications of Radian Measure 3.3 The Unit Circle and Circular Functions.

Higher MathematicsHigher Mathematics Trigonometry hsn.uk.net Page 1 CfE Edition Trigonometry 1 Radians EF Degrees are not the only units used to measure angles. The radian (RAD on

Higher MathematicsHigher Mathematics Trigonometry hsn.uk.net Page 1 CfE Edition Trigonometry 1 Radians EF Degrees are not the only units used to measure angles. The radian (RAD on