Transcript 7.1 Basic Trigonometric Identities

Warm-Up 2/12
Evaluate – this is unit circle stuff, draw your triangle.
2

1.
1.sin
4
2
2.Cos 1 (1)
3.Tan 1 (1)  Cos 1 (
2.
3
)
2
13
3.
12
7.1 Basic Trigonometric Identities
Trig Identity: a trig expression that is true for
all values of the variables
Reciprocal Identities
1
sin  
csc 
1
cos  
sec 
1
csc  
sin 
1
sec  
cos 
1
tan  
cot 
1
cot  
tan 
Quotient Identities
sin 
cos 
 tan 
 cot 
cos 
sin 
Pythagorean Identities
sin 2   cos 2   1
tan   1  sec 
2
2
1  cot 2   csc2 
This is the most basic all are
derived from it.
Divide everything by cos2
Divide everything by sin2
Opposite angle Identities
sin( A)   sin A
cos( A)  cos A
Examples
Use the given info to find the trig value.
3
1. If sec   , find cos .
2
Since
cos
2
cos  
3
and
sec
are reciprocals,
2. If
4
csc   , use the identities to find tan
3
1  cot   csc 
2
2
4
1  cot    
3
16
2
1  cot  
9
7
2
cot  
9
2
2
7
cot   
3
Use an identity that involves given info.
Then
Substitute what you know.
Move the 1 to the right side. Change
it to 9/9.
3
3 7
tan   

7
7
Express each value as a trigonometric function of an angle in
Quadrant I.
3.
sin 600  sin 240
2
Subtract 360 or 2 if in radians
Draw everything you know.
Then draw the same reference
angle in the first quadrant.
 3
-1
60
3
60
1
2
negative
Sine is ____________
in the 3rd quadrant
So If I have to write it as an angle in the 1st quadrant will it
be the same or will I have to take the opposite?
Take the opposite, so your final answer is
-sin60o
If the original problem is in radians your final answer must
be in radians, if it is degrees, your final answer will be in
degrees.
Try these:
19
1.sin
4
Check:
1.sin

4
2.cos(410)
2.cos50
37
3.tan
6
3.tan

6
If the original problem is in radians your final answer must
be in radians, if it is degrees, your final answer will be in
degrees.
Simplify
sin x  sin x cot x
2
sin x(1  cot 2 x)
2
sin x(csc x)
Is there a GCF? Yes sinx
Factor
Use your identities, look back at your
notes 1+cot2x = csc2x
 1 
sin x  2  Write csc x in terms of sin x,
 sin x 
1
sin x
 csc x
Simplify completely  done
7.1 Assignment
p. 428 # 25 – 35, 45 – 53 odds
Must use the identities for #25 - 35