Angles and Radian Measures: Classnotes, G. Battaly
© G. Battaly 2016 1
April 19, 2016
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Study 5.1 CVC # 17; #147; 51, 5763; 7175College Algebra & Trig Home Page
Homework
GOALS:1. Understand that angles have measures in degrees or radians.2. There are 360 = 2π radians in a complete circle. 1 radian subtends an arc = radius of the circle.3. Trig functions of an angle are defined as ratios of: the sides of the associated triangle; or the coordinates of pt. (x,y) and the radius, r for a circle with C(0,0)4. Signs (+ or ) of trig functions are determined by the quadrant with the terminal ray.5. To convert degrees to radians mult. by π / 180 . To convert radians to degrees mult. by 180 / π.
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
basic_angles.mp4
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Angles and Radian Measures: Classnotes, G. Battaly
© G. Battaly 2016 2
April 19, 2016
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
+ θ
basic_angles.mp4
θ
Angle in standard postion:1. initial side on pos. xaxis2. vertex (0, 0)
Angle is:θ > 0 if counterclockwise θ
Angles and Radian Measures: Classnotes, G. Battaly
© G. Battaly 2016 3
April 19, 2016
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
= 0.5 1 = 0.87 1 = 0.5 0.87
csc θ = 1 0.5sec θ = 1 0.87 cot θ =0.87 0.5
sin θ = y rcos θ = x rtan θ = y x
( x, y )
r
trig_functions_unitCircle.mp4
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
sin θ = y rcos θ = x rtan θ = y x
csc θ = r ysec θ = r xcot θ = x y
trig_functions_unitCircle.mp4
Definitions of Trig. Functions
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Angles and Radian Measures: Classnotes, G. Battaly
© G. Battaly 2016 4
April 19, 2016
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
basic_angles.mp4
sin θ cos θ tan θ
III
III IV
sin θ cos θ tan θ
sin θ cos θ tan θ
sin θ cos θ tan θ
Which are positive? Which negative?
sin θ = y rcos θ = x rtan θ = y x
csc θ = r ysec θ = r xcot θ = x y
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
basic_angles.mp4
sin θ cos θ tan θ
csc θ = r ysec θ = r xcot θ = x y
III
III IV
sin θ cos θ tan θ
sin θ cos θ tan θ
sin θ cos θ tan θ
Which are positive? Which negative?
+
+
+++
+
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Angles and Radian Measures: Classnotes, G. Battaly
© G. Battaly 2016 5
April 19, 2016
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
basic_angles.mp4
Circumference: C = 2 π r
C = 2 π r
The circumference of a circle is a measure of the length around the whole circle.
If r = 1, what is the length around the whole circle?_____what is the length around half of the circle? ________
around one quarter of the circle? ________
A sector of a circle is the linear measure of part of the circumference.
s = r θ θ in radians
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
basic_angles.mp4
Circumference: C = 2 π r
C = 2 π r
The circumference of a circle is a measure of the length around the whole circle.
If r = 1, what is the length around the whole circle?_____what is the length around half of the circle? ________around one quarter of the circle ________
A sector of a circle is the linear measure of part of the circumference.
s = r θ θ in radians
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Angles and Radian Measures: Classnotes, G. Battaly
© G. Battaly 2016 6
April 19, 2016
r
r
s = r
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
basic_angles.mp4
Radian: angle that subtends an arc of length = r of the circle
degrees radians
0 0
90 2
180
270 3 2
s = r θ θ in radians
r
r
s = r
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
basic_angles.mp4
Radian: angle that subtends an arc of length = r of the circle
degrees radians
0 0
90 2
180
270 3 2
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Angles and Radian Measures: Classnotes, G. Battaly
© G. Battaly 2016 7
April 19, 2016
r
r
s = r
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
basic_angles.mp4
Convert from Degrees to Radians: Multiplication Property of 1: multiply by / 180
Convert 45 to radians
r
r
s = r
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
basic_angles.mp4
Convert from Degrees to Radians: Multiplication Property of 1: multiply by / 180
Convert 45 to radians
http://www.battaly.com/algebra_trig/http://www.battaly.com/algebra_trig/homework/5_1_angles.htmhttp://www.battaly.com/algebra_trig/http://www.battaly.com/algebra_trig/homework/5_1_angles.htm
Angles and Radian Measures: Classnotes, G. Battaly
© G. Battaly 2016 8
April 19, 20165.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
basic_angles.mp4
Label the angles in degrees and radians.
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
basic_angles.mp4
Label the angles in degrees and radians.
http://www.battaly.com/algebra_trig/http://www.battaly.com/algebra_trig/homework/5_1_angles.htmhttp://www.battaly.com/algebra_trig/http://www.battaly.com/algebra_trig/homework/5_1_angles.htm
Angles and Radian Measures: Classnotes, G. Battaly
© G. Battaly 2016 9
April 19, 20165.1 Angles and Radian Measure
College Algebra & Trig Home Page Homework
basic_angles.mp4
Label the angles in degrees and radians.
Class Notes: Prof. G. Battaly, Westchester Community College, NY
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
basic_angles.mp4
Label the angles in degrees and radians.
http://www.battaly.com/algebra_trig/http://www.battaly.com/algebra_trig/homework/5_1_angles.htmhttp://www.battaly.com/algebra_trig/http://www.battaly.com/algebra_trig/homework/5_1_angles.htm
Angles and Radian Measures: Classnotes, G. Battaly
© G. Battaly 2016 10
April 19, 20165.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
Convert to radians: 60
Hint: Use the multiplication property of 1.
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
Convert to radians: 60
Hint: Use the multiplication property of 1.
http://www.battaly.com/algebra_trig/http://www.battaly.com/algebra_trig/homework/5_1_angles.htmhttp://www.battaly.com/algebra_trig/http://www.battaly.com/algebra_trig/homework/5_1_angles.htm
Angles and Radian Measures: Classnotes, G. Battaly
© G. Battaly 2016 11
April 19, 2016
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
Convert to radians: 150
Hint: Use the multiplication property of 1.
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
Convert to degrees: 7π Which quadrant? 4
Hint: Use the multiplication property of 1.
http://www.battaly.com/algebra_trig/http://www.battaly.com/algebra_trig/homework/5_1_angles.htmhttp://www.battaly.com/algebra_trig/http://www.battaly.com/algebra_trig/homework/5_1_angles.htm
Angles and Radian Measures: Classnotes, G. Battaly
© G. Battaly 2016 12
April 19, 2016
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
Convert to degrees: 7π Which quadrant? 4
Hint: Use the multiplication property of 1.
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
G: 415 F: positive angle
Angles and Radian Measures: Classnotes, G. Battaly
© G. Battaly 2016 13
April 19, 2016
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
Length of a Circular Arc: s = r θ, θ in radians
G: r = 16 in, θ = 60 , F: s
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
Length of a Circular Arc: s = r θ, θ in radians
G: r = 9 yds, θ = 315 F: s
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Angles and Radian Measures: Classnotes, G. Battaly
© G. Battaly 2016 14
April 19, 2016
5.1 Angles and Radian Measure
Class Notes: Prof. G. Battaly, Westchester Community College, NY
College Algebra & Trig Home Page Homework
Length of a Circular Arc: s = r θ, θ in radians
G: r = 9 yds, θ = 315 F: s
http://www.battaly.com/algebra_trig/http://www.battaly.com/algebra_trig/homework/5_1_angles.htm
Attachments
basic_angles.mp4
trig_functions_unitCircle.mp4
Gertrude Battaly
SMART Notebook
Gertrude Battaly
SMART Notebook
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