8-4
Sine, Cosine, and Tangent Ratios
Chapter 8 Section 4
Mrs. Brook 
Vocabulary


Trigonometry
Derived from Greek
words meaning “triangle
measurement”
Triangle
terminology
Opposite side: the side opposite the
angle
angle
opposite
opposite
angle
opposite
opposite
angle
angle
Adjacent side: the side beside the
angle
adjacent
angle
adjacent
adjacent
angle
adjacent
angle
angle
Hypotenuse: the longest side
and across from the right angle
SOH CAH TOA

SOH

CAH

TOA
You need to memorize this!!! Use SOH
CAH TOA to help you remember these
ratios!!!
Definitio
ns
B
c
a
90o
A
b
C
Sine of angle A
sin(A) =
opposite
=
hypotenuse
a
c
B
c
a
A
90o
b
C
Sine of angle B
sin(B) =
opposite
=
hypotenuse
b
c
B
c
a
A
90o
b
C
Cosine of angle A
cos(A) =
adjacent
=
hypotenuse
b
c
B
c
a
A
90o
b
C
Cosine of angle B
cos(B) =
adjacent
=
hypotenuse
a
c
B
c
a
90o
A
b
C
Tangent of angle A
tan(A) =
opposite
=
adjacent
a
b
B
c
A
a
90o
b
C
Tangent of angle B
tan(B) =
opposite
=
adjacent
b
a
B
c
A
a
90o
b
C
Write the Sin, Cos, and Tan
Ratios for angle A
SOH CAH TOA
A
Sin A = 7/25
25
24
Cos A = 24/25
B
C
7
Tan A = 7/24
Try this one 
Sin E
SOH CAH TOA
6/10 = 3/5
Sin F
Cos E 8/10 = 4/5 Cos F
Tan E
6/8 = 3/4
Tan F
8/10 = 4/5
6/10 = 3/5
8/6 = 4/3
Find the value of x using Trig.
Note: If “x” is on top - multiply; If “x” is on bottom - divide!!
Remember: SOH CAH TOA
THIS IS JUST THE ANGLE!!
Since we have an
O & A we use Tan
(no hypotenuse!)
64
7
X
------
Tan 64 = x/7
Since x is on top, mult.
Type 7 * tan 64 in calc.
67
x
6
------
Since we have an
O & A we use Tan
(no hypotenuse!)
Tan 67 = 6/x
Since x is on bottom divide.
Type 6 divided by tan 67 in calc
35
----
X
20
Since we have an
O & H we use Sin
Sin 35 = x/20
Since x is on top, mult.
Type 20 * sin 35 in calc.
Since we have an
A & H we use Cos
62
50
Cox 62 = 50/x
-----x
Since x is on bottom divide
Type 50 divided by cos 62
in calc.
Find the value of x degrees using
When finding an angle measure use “inverse” Trig. or
Trig. Note:
the 2nd button!!
Remember: SOH CAH TOA
Since we have an
O & A we use Tan
(no hypotenuse!)
x
3
9
____
Tan x = 9/3
71.6
Since we have an
A & H we use Cos
x
16
----20
Cos x = 16/20
36.9
Since x is the angle, use the 2nd button!
Since x is the angle, use the 2nd button!
Type 2nd Tan, then 9/3 using the n/d button. Type 2nd Cos, then 16/20 using the n/d
button.
Since we have an
O & H we use Sin
x
____
4
5
Sin x = 4/5
53.1
Since x is the angle, use the 2nd
button!
Type 2nd Sin, then 4/5 using the n/d
button.
What have I learned?
SOH CAH TOA
If “x” is on bottom “divide”
If “x” is on top “multiply”
If solving for a side use regular sin, cos, or tan
If solving for an angle use inverse sin, cos, or
tan
Here’s your daily joke 

Why didn’t sin and tan go to the party?
Just cos
Ha! Ha! 