Download CH. 4 – TRIGONOMETRIC FUNCTIONS 4.3 – Right Triangle Trig

CH. 4 – TRIGONOMETRIC
FUNCTIONS
4.3 – Right Triangle Trig
SOH CAH TOA!!!

Recall your right triangle trig facts:
opp
sin  
hyp

adj
cos  
hyp
opp
tan  
adj
Ex: Find the exact values of the six trig functions of
θ.








cos θ = 4/5
sec θ = 5/4
Use Pythagorean Theorem!
Opposite side = 3
sin θ = 3/5
tan θ = 3/4
csc θ = 5/3
cot θ = 4/3
5
3

4
SOH CAH TOA!!!

Ex: Find the exact values of the six trig functions of θ
if sinθ = 5/6 and 0 < θ < 90°.




Draw a right triangle and label known information!
sin θ = 5/6
csc θ = 6/5
Use Pythagorean Theorem to find the third side!

Leave it in reduced radical form!
11
cos  
6
5
5 11
tan  

11
11
6
6 11

sec  
11
11
11
cot  
5
5
6

11
IF
8
sin  
17 , WHAT TRIG FUNCTION WILL
GIVE A VALUE OF
1.
tanθ
2.
cotθ
3.
cosθ
4.
cscθ
5.
secθ
15 ?
8
tan   2 , WHAT TRIG FUNCTION WILL
GIVE A VALUE OF 5 ?
IF
1.
sinθ
2.
cotθ
3.
cosθ
4.
cscθ
5.
secθ
IF
1.
2
sin   , FIND THE cos
5
3
5
2.
3.
29
5
4.
5.
5
2
.
21
2
21
5
0%
0%
0%
0%
0%
3
IF sin  
, FIND THE csc 
6
1.
33
6
2.
3.
99
3
6 3
4.
5.
.
2 3
6
3
0%
0%
0%
0%
0%
IF
1.
sec   3 , FIND THE tan 
2 2
2.
3.
2
2
4.
5.
.
3
2
2 2
3
2
4
0%
0%
0%
0%
0%
7
IF cot  
, FIND THE csc 
9
1.
2.
3.
4.
5.
74
7
.
88
9
2 22
9
2 154
7
9 22
2
0%
0%
0%
0%
0%
TRIG IDENTITIES!!!

Ex: Use trig identities to verify the equation:
cos tan   sin 

You’re being asked to prove this equation is true, so work
one side out until it looks like the other side.


Tip: Work out the more complex side!
Strategy #1: Convert everything to sin and cos
cos tan 
 sin 
sin 
cos 
cos 
sin 
 sin 
TRIG IDENTITIES!!!

Ex: Use trig identities to verify the equation:
(1  sin  )(1  sin  )  cos 2 

Strategy #2: Make a substitution using the identity sin2
θ + cos2 θ = 1
(1  sin  )(1  sin  )
1 sin 2 
 cos 2 
 cos 2 
1  sin 2   sin 2   cos 2   sin 2 
1
1

4
Find the 6 trigonometric functions for  
3
.
sin  
cos 
 3
2
csc  2 3
1

2
sec  2
 3
3
2
tan    1
2
 3
cot  
1
3
2

3
 3
2

13

Find the 6 trigonometric functions for  
 6 
2
2
.
1
csc 
cos  0
sec 
sin  
tan  
1
0
 undefined
cot  
1
undefined
0
1
0

Find the 6 trigonometric functions for some angle
θ in the 1st quadrant.
csc 
3 5
5
cos 
2
3
sec 
3
2
tan  
5
2
cot  
2 5
5
sin  
5
3

Find the 6 trigonometric functions for some angle
θ in the 2nd quadrant.
sin  
cos 
1
5
csc  5
2 6

5
1
tan    2 6
6

12
sec 
5
5 6

 
12
2 6
cot   2 6