trigo

1. The Trigonometric Functions
we will be looking at
SINE
COSINE
TANGENT

2. The Trigonometric Functions
SINE
COSINE
TANGENT

3. SINE
Pronounced
“sign”

4. Pronounced
“co-sign”
COSINE

5. Pronounced
“tan-gent”
TANGENT

6. Prounounced
“theta”
Greek Letter q
Represents an unknown angle

7. q
opposite
hypotenuse
Sin
Opp
Hyp

Leg
adjacent
Cos
Adj
Hyp

Leg
Tan
Opp
Adj

Leg
Leg
hypotenuse
opposite
adjacent

8. We need a way to remember all of
these ratios…

9. Old Hippie
Some
Old
Hippie
Came
A
Hoppin’
Through
Our
Apartment

10. SOHCAHTOA
Old Hippie
Sin
Opp
Hyp
Cos
Adj
Hyp
Tan
Opp
Adj

11. Finding sin, cos, and
tan.
(Just writing a ratio or decimal.)

12. Find the sine, the cosine, and the tangent of angle A.
Give a fraction and decimal answer (round to 4 places).
hyp
opp
A 
sin
8
.
10
9
 8333
.

hyp
adj
A 
cos
8
.
10
6
 5556
.

adj
opp
A 
tan
6
9
 5
.
1

9
6
10.8
A
Shrink yourself
down and stand
where the angle is.
Now, figure out your ratios.

13. Find the sine, the cosine, and the tangent of angle A
A
24.5
23.1
8.2
hyp
opp
A 
sin
5
.
24
2
.
8
 3347
.

hyp
adj
A 
cos
5
.
24
1
.
23

9429
.

adj
opp
A 
tan
1
.
23
2
.
8
 3550
.

Give a fraction and
decimal answer (round
to 4 decimal places).
Shrink yourself
down and stand
where the angle is.
Now, figure out your ratios.

14. Finding a side.
(Figuring out which ratio to use and
getting to use a trig button.)

15. Ex: 1 Figure out which ratio to use. Find
x. Round to the nearest tenth.

55
20 m
x
 
20
55
tan
x

m
6
.
28

x
  x

55
tan
20
tan
20 55 )
Shrink yourself
down and stand
where the angle is.
Now, figure out
which trig ratio
you have and set
up the problem.

16. Ex: 2 Find the missing side. Round to the
nearest tenth.

72
80 ft
x
 
x
80
72
tan 
ft
26

x
  80
72
tan 
x
 
 
72
tan
80

x
tan
80 72 =
 ( ) )
Shrink yourself down and
stand where the angle is.
Now, figure out which trig ratio
you have and set up the problem.

17. Ex: 3 Find the missing side. Round to the
nearest tenth.

24
283 m
x  
283
24
sin
x

m
1
.
115

x
  x

24
sin
283
Shrink yourself
down and stand
where the angle is.
Now, figure out
which trig ratio
you have and set
up the problem.

18. Ex: 4 Find the missing side. Round to the
nearest tenth.

40
20 ft x  
20
40
cos
x

ft
3
.
15

x
  x

40
cos
20

19. Finding an angle.
(Figuring out which ratio to use and getting to use
the 2nd button and one of the trig buttons.)

20. Ex. 1: Find q. Round to four decimal places.
9
17.2
Make sure you are in degree mode (not radians).
9
2
.
17
tan 
q
q
2nd tan 17.2  9

 3789
.
62
q
)
Shrink yourself down and stand where
the angle is.
Now, figure out which trig ratio you have
and set up the problem.

21. Ex. 2: Find q. Round to three decimal places.
23
7
Make sure you are in degree mode (not radians).
23
7
cos 
q
q
2nd cos 7  23

 281
.
72
q
)

22. Ex. 3: Find q. Round to three decimal places.
200
Make sure you are in degree mode (not radians).
400
200
sin 
q
q
2nd sin 200  400

 30
q
)

23. When we are trying to find a side
we use sin, cos, or tan.
When we are trying to find an angle
we use sin-1, cos-1, or tan-1.