Scribd
Upload
24 views11 pages

Section 5.1

This document discusses trigonometric identities. It introduces quotient, reciprocal, and negative-angle identities. It then derives the Pythagorean identities from the unit circle definition of trigonometric functions. Examples are provided to demonstrate using the newly learned identities to find trigonometric function values given one value and the quadrant.

Uploaded by

Dalia Eldeab
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPT, PDF, TXT or read online on Scribd
24 views11 pages

Section 5.1

This document discusses trigonometric identities. It introduces quotient, reciprocal, and negative-angle identities. It then derives the Pythagorean identities from the unit circle definition of trigonometric functions. Examples are provided to demonstrate using the newly learned identities to find trigonometric function values given one value and the quadrant.

Uploaded by

Dalia Eldeab
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPT, PDF, TXT or read online on Scribd
You are on page 1/ 11

Do Now

Chapter 5
Trigonometric Identities
Section 5.1
Fundamental Identities
Objective:
SWBAT use the fundamental identities of
Trigonometry functions to find trigonometric functions
values given one value and the quadrant.
Trigonometric Identities
Quotient Identities: (write these down on an index card)

sin  cos 
tan   cot  
cos  sin 
Reciprocal Identities:
1 1
sin   cos  
1
tan  
csc  sec  cot 
1 1 1
cot   sec  csc 
tan  cos sin 
Trigonometric Identities Cntd.
(write these down on an index card)

Negative-Angle Identities:

sin( )   sin  cos(  )  cos  tan(  )   tan 


csc( )   csc sec( )  sec cot(  )   cot 
Where did our Pythagorean Identities come from?
Do you remember the Unit Circle?
What is the equation for the unit circle?
x2 + y2 = 1
What does x = ? What does y = ?
(in terms of trig functions)
Sin2 θ + cos2 θ = 1

Pythagorean
Identity!
Take the Pythagorean Identity and
discover a new one!
Hint: Try dividing everything by cos2θ
sin2θ + cos2θ = 1 .
cos2θ cos2θ cos2θ

tan2θ + 1 = sec2θ
Quotient Reciprocal
Identity another Identity
Pythagorean
Identity
Take the Pythagorean Identity and
discover a new one!
Hint: Try dividing everything by sin2θ
sin2θ + cos2θ = 1 .
sin2θ sin2θ sin2θ
1 + cot2θ = csc2θ

Quotient Reciprocal
Identity a third Identity
Pythagorean
Identity
Using the identities you now know, find the trig
5 value :
If tan    and  is in quadrant II, find sec .
3
tan 2   1  sec 2 
2
Look for an identity  5

 3   1  sec 2

that relates tangent and
secant. 25
 1  sec 2 
9
tan 2   1  sec 2  34
 sec 2 
9
34
sec   
9
34
sec   
3
Using the identities you now know, find the trig
value :
If tan    5 and  is in quadrant II, find cot ()
3

1
cot( ) 
tan( )
1
cot( ) 
 tan 
1 3
cot( )  
  3  5
5
Using the identities you now know,
find the trig value.
1.) If cosθ = 3/5, find csc θ.
sin 2   cos2   1
3 
2

sin 2      1
5 
25 9
sin 2   
25 25
16
sin  
2

25
4
sin   
5

1 1 5
csc    
sin   4 4
5
Using the identities you now know, find
the trig value.
2.) If cosθ = 3/4, find secθ

1 1 4
sec    
cos 3 3
4

You might also like