Download Trigonometry Notebook

Trigonometry Notebook
*
Use the provided sheets.
*
This notebook should be your best written work. Quality counts in this project.
Proper notation and terminology is important.
We will follow the order used in class.
Anyone in a Trigonometry course should to be able to read and understand your material.
*
You are encouraged to provide examples for your own benefit when using this in the future.
There may not be sufficient space to neatly put them on the page itself. Use the back or other paper.
These items need to be included in the notebook.
Follow the order listed.
1.
Definitions of sine and cosine based on the unit circle.
Definitions of tangent, cotangent, secant, and cosecant based on sine and cosine.
2.
A completed Unit Circle, Trigonometric Table, and master list of all ‘key’ trigonometric identities.
3.
Complete and accurate graphs of all six trigonometric functions.
(List domain, range, and period for all graphs and the amplitude on the applicable graphs.)
4.
Complete and accurate graphs of the two types of inverses for each trigonometric function.
(example:
x = siny and y = arcsinx )
The two types of inverses will be on the same graph together but should be clearly labeled.
List the Domain and Range for both types of inverses.
5.
Prove the common identities. (The list will be provided to you.)
6.
Right triangle definitions of the six trigonometric functions
(You must include a visual/picture connection between the unit circle definitions of sine, cosine, tangent
and SohCahToa.)
7.
Derive the formulas for area of a non right triangle. (Include the related diagram.)
8.
Prove the laws of sines and cosines. (Include the related diagram.)
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Trigonometry Notebook
1.
Definitions of sine and cosine based on the unit circle.
Definitions of tangent, cotangent, secant, and cosecant based on sine and cosine.
2
Trigonometry Notebook
2.
Unit Circle.
For each ‘key’ point on the unit circle, include the degrees, radians, and coordinates of the associated points.
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Trigonometry Notebook
2.
Complete the Trigonometric Table.
Radians
 2
Degrees
0,  
 2 , 2 
  2 , 2 
0,  
 2 , 2 
 0,  
cos
sin 
tan 
sec
csc
cot 
0

2

3
2
2
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Trigonometry Notebook
2.
Write in each identity.
pythagorean identities (all three)
cos(-A) = cos A
sin(-A) = - sin A
cos(A + B) =
cos(A – B) =
cos2    =
sin2    =
sin(A + B) =
sin(A – B) =
tan (A + B) =
tan (A – B) =
cos 2A =
=
=
sin 2A =
tan 2A =
Power Reducing Identities:
cos 2  
sin 2  
cos2 =
sin2 =
tan2 =
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Trigonometry Notebook
3.
Complete and accurate graphs of all six trigonometric functions.
(List domain, range, and period for all graphs and the amplitude on the applicable graphs.)
y  csc 
y  sin 
D:
R:
R:
y  tan 
D:
R:
y  sec 
y  cos 
D:
D:
D:
R:
y  cot 
R:
D:
R:
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Trigonometry Notebook
4.
Complete and accurate graphs of the two types of inverses for each trigonometric function.
(example:
x = siny and y = arcsinx )
The two types of inverses will be on the same graph together but should be clearly labeled.
List the Domain and Range for both types of inverses.
7
Trigonometry Notebook
5.
Prove the common identities. (Follow the order shown. Include a picture if * is shown.)
*pythagorean identities (all three)
*cos(-A) = cos A
*sin(-A) = - sin A
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Trigonometry Notebook
5.
Prove the common identities.
* cos( A  B)  cos A cos B  sin A sin B
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Trigonometry Notebook
5.
Prove the common identities.
cos( A  B)  cos A cos B  sin A sin B
cos  2     sin 
sin  2     cos
sin( A  B)  sin A cos B  cos A sin B
sin( A  B)  sin A cos B  cos A sin B
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Trigonometry Notebook
5.
Prove the common identities.
tan( A  B) 
tan A  tan B
1  tan A tan B
tan( A  B) 
tan A  tan B
1  tan A tan B
cos(2 A)  cos2 A  sin 2 A
= 2 cos 2 A  1
= 1  2sin 2 A
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Trigonometry Notebook
5.
Prove the common identities.
sin 2 A  2sin Acos A
tan 2 A 
2 tan A
1  tan 2 A
Power Reducing Identities:
cos2   12 1  cos 2 
sin 2   12 1  cos 2 
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Trigonometry Notebook
5.
Prove the common identities.
cos2 =
sin2 =
tan  2   
sin A
1  cos A
1  cos 
=
=
1  cos A
sin A
1  cos 
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Trigonometry Notebook
6.
Right triangle definitions of the six trigonometric functions
(You must include a visual/picture connection between the unit circle definitions of sine, cosine, tangent
and SohCahToa.)
14
Trigonometry Notebook
7.
Derive the formulas for area of a non right triangle. (Include the related diagram.)
15
Trigonometry Notebook
8.
Prove the laws of sines and cosines. (Include the related diagram.)
16