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Transcript 
TRIGONOMETRY
Trigonometry
is the study of
triangles.
Opposite

Adjacent
Opposite

Adjacent
Opposite
Adjacent

The Ratio of the Opposite side and the
Hypotenuse is called sine (or sin)
The Ratio of the Adjacent
side and the Hypotenuse is
called cosine (or cos)
The Ratio of the
Opposite side and
the Adjacent side
is called tangent
(or tan)

Adjacent
Opposite
Trigonometric Ratios
Adj
Cos  =
Hyp
Opp
Tan  =
Adj
Opposite
Opp
Sin  =
Hyp

Adjacent
Adj
Cos  =
Hyp
sohcahtoa
Opp
Sin  =
Hyp
Opp
Tan  =
Adj
e.g. Find Sin , Cos  & Tan 
Adj
20
Cos  =
=
Hyp
29
21 m
Opp
21
Sin  =
=
Hyp
29

20 m
Opp
21
Tan  =
=
Adj
20
e.g. If sin  = ½ , find
m

x
x.
Opp
Sin  = Hyp
1 =
2
20
x
x x 20
20 x 1 =
2
20
x = 10 m
e.g. find the value of
calculator.
x
m
x using your
Opp
Sin  = Hyp
Using a calculator sin 30˚ = 0.5
30˚
x
x8
8 x 0.5 =
8
x = 4m
Opposite

Adjacent
Opp
Sin  =
Hyp
Adj
Cos  =
Hyp
Opp
Tan  =
Adj
e.g. find the value of
calculator.
x
m
x using your
Opp
Sin  = Hyp
Sin 30˚ =
x
8
Using a calculator, sin 30˚ = 0.5
30˚
x
x8
8 x 0.5 =
8
x = 4m
Opposite

Adjacent
Opp
Sin  =
Hyp
Adj
Cos  =
Hyp
Opp
Tan  =
Adj
What do you do if the denominator
is the missing side?
x
e.g.
30˚
8
x Adj
30˚
1. Identify the sides
2. Choose the trig ratio
Opp
Tan  =
Adj
3. Substitute given values
Tan 30 =
x
8
8
Opp
4. Use calculator to find tan 30
0.5774 =
x
8
5. Swap 0.5774 and
x
6. Solve
8
=
0.5774
x = 13.86
x
If we know the lengths of any two sides in a right
angle triangle, we can calculate the size of any
angle in it
e.g.1
1. Name the sides
2. Choose the correct trig ration
Adj
Cos  =
Hyp

9 Adj
1. Name the sides
2. Choose the correct trig ration
Adj
Cos  =
Hyp
3. Enter the given data
9
Cos  =
15

9 Adj
4. Calculate the angle by using the “inverse ratio”
button on the calculator. i.e. cos-1
=
Cos-1
9
15
  = 53.13˚
1. Name the sides
2. Choose the correct trig ration

Opp
Sin  =
Hyp
3. Enter the given data
9
Sin  =
15
9 Opp
4. Calculate the angle by using the “inverse ratio”
button on the calculator. i.e. sin-1
=
Sin-1
9
15
  = 36.87˚
Opposite

Adjacent
Opp
Sin  =
Hyp
Adj
Cos  =
Hyp
Opp
Tan  =
Adj
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