Trigonometry Ratios

1
Trigonometry Ratios
What are the ones we know so far and are there
any more?
2
When you were first introduced to Trigonometry
Tan ? ?
It was
Cos ? ?
adjacent
adjacent
Sin? ?
OR
OR
Hypotenuse
opposite
Hypotenuse
And then you used them to find the unknown side
or angle
opposite
But why limit ourselves to comparing the sides in
these ways?
3
You remembered all of this by
S
O
H
C
A
H
T
O
A
OR
Silly Old Hags Cant Always Hide Their Old Age.
What would happen if we compared the sides
differently to SOHCAHTOA?
4
Instead of comparing
Why not compare
OPPOSITE
to
ADJACENT
ADJACENT
to
OPPOSITE
ADJACENT
OPPOSITE
which is Tan ??
5
But if we compare the sides this way
The Tan ratio is
This new way of comparing these sides is the.
RECIPROCAL
of the Tan Ratio
is remembered as
the Cotangent Ratio
The same thing can be done for Sine Cosine
is the Reciprocal of the Cosine Ratio
is remembered as
the Secant Ratio
is the Reciprocal of the Sine Ratio
is remembered as
the Cosecant Ratio
6
How can these new ratios be used?
You can be given a triangle and asked to simply
give the value of the Cotangent, Secant or
Cosecant of an angle, expressed as a fraction
You can also be asked to give the EXACT VALUE of
the Cotangent, Secant or Cosecant of an angle.
e.g.
Find the value of Secant 30?
e.g.

Sec 30?
What is the value of Cosec B?

Cosec B
Remember you can only be asked for an exact value
if the angle is related to 30?, 45? or 60?
7
You could be asked to find the Cotangent, Secant
or Cosecant of an angle for which you would
normally use your calculator
And lastly
Find the value of Secant 37?
e.g.
Unfortunately, there are no calculator keys for
these ratios!
?
So you have to find the decimal value from
calculator and then either use the reciprocal key
or store it in the calculators memory and then
divide it into 1
1
Sec 37?

Cos 37?
?
?
1.252
to 3 d.p.