Download 9.5 Trigonometric Ratios

9.5 Trigonometric Ratios
Sin-Cos-Tan
What is Trigonometry?
• Trigonometry (from Greek trigōnon "triangle" +
metron "measure") is a branch of mathematics
that studies triangles and the ratios between
their sides and the angles between these sides.
The field evolved during the third century BC as
a branch of geometry used extensively for
astronomical studies. It is also the foundation of
the practical art of surveying.
http://en.wikipedia.org/wiki/Trigonometry
Right Angle Trigonometry
The Ratio used in Right Angle Trigonometry
are
Sine – Sin
c
Cosine – Cos
a
Tangent - Tan
b
Right Angle Trigonometry
The Ratio used in Right Angle Trigonometry
a
Sin A 
c
b
Cos A 
c
a
Tan A 
b
c
a
b
Right Angle Trigonometry
The Ratio used in Right Angle Trigonometry
opposite
SinA 
hypotenuse
adjacent
CosA 
hypotenuse
opposite
TanA 
adjacent
c
a
b
Right Angle Trigonometry
The Ratio used in Right Angle Trigonometry
opposite
SinA 
 SOH
hypotenuse
adjacent
CosA 
 CAH
hypotenuse
opposite
TanA 
 TOA
adjacent
c
a
b
How to Remember the Ratio
Chief SOH – CAH - TOA
opposite
SinA 
 SOH
hypotenuse
adjacent
CosA 
 CAH
hypotenuse
opposite
TanA 
 TOA
adjacent
Right Angle Trigonometry
The Ratio used in Right Angle Trigonometry
B
5
Sin A   .3846
13
12
Cos A   .9231
13
5
Tan A   .4167
12
13
A
12
5
C
Right Angle Trigonometry
The Ratio used in Right Angle Trigonometry
B
2.5
Sin A 
 .3846
6.5
6
Cos A 
 .9231
6.5
2.5
Tan A 
 .4167
6
13
5
6.5
A
2.5
6
12
C