1. TRIGONOMETRY

2. Trigonometry is the study of triangles.

3. Opposite
Hypotenuse 
Adjacent

4. Opposite
Hypotenuse 
Adjacent

5. Adjacent
Hypotenuse 
Opposite

6. Trigonometric Ratios
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)
Opposite
Hypotenuse
The Ratio of the Opposite side and the Adjacent side is called tangent (or tan) 
Adjacent

7. Opp Sin  = Hyp Adj Cos  = Hyp Opp Tan  = Adj Hypotenuse Opposite 
Adjacent
Opp
Adj
Tan  =

8. Adj
Hyp
Cos  =
sohcahtoa
Opp
Adj
Opp
Hyp
Tan  =
Sin  =

9. e.g. Find Sin , Cos  & Tan  Opp Hyp 21 29 Sin  = = Adj Hyp 20 29
29 m
21 m
Adj
Hyp 20 29
Cos  = = 
20 m
Opp
Adj 21 20
Tan  = =

10. x x x x x e.g. If sin  = ½ , find . Opp Hyp Sin  = 1 2 20 = 20 x 1 2m
Sin  = x 1 2 20 =  x
20 m
20 x 1 2
x 20 = 20 x
= 10 m

11. x x x x e.g. find the value of using your calculator. Opp Hyp Sin  =m
Using a calculator sin 30˚ = 0.5 x
x 8
8 x
0.5 =
30˚ 8
8 m x
= 4 m

12. Opp Adj Opp Hyp Adj Hyp Tan  = Sin  = Cos  = Hypotenuse Opposite 
Adjacent
Opp
Adj
Opp
Hyp
Adj
Hyp
Tan  =
Sin  =
Cos  =

13. x x x x x e.g. find the value of using your calculator. Opp Hyp8 m
Sin 30˚ =
Using a calculator, sin 30˚ = 0.5 x
30˚
8 m
x 8
8 x
0.5 = 8 x
= 4 m

14. Opp Adj Opp Hyp Adj Hyp Tan  = Sin  = Cos  = Hypotenuse Opposite 
Adjacent
Opp
Adj
Opp
Hyp
Adj
Hyp
Tan  =
Sin  =
Cos  =

15. What do you do if the denominator is the missing side?
e.g. x
30˚ 8

16. x x 8 Adj Opp Opp Tan  = Adj 8 Tan 30 = 30˚ 1. Identify the sides
2. Choose the trig ratio
Opp
Adj
Tan  =
3. Substitute given values 8 x
Tan 30 =

17. x x x x 8 0.5774 = 8 = 0.5774 = 13.86 4. Use calculator to find tan 30
5. Swap and x 8 =
0.5774
6. Solve x
= 13.86

18. Opp Sin  = Hyp Adj Cos  = Hyp 15  9
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
Opp
Hyp
Hyp
Sin  = 15
2. Choose the correct trig ration
Adj
Hyp
Cos  =  9
Adj

19.  Adj Cos  = Hyp 9 Cos  = 15 9  = Cos-1 15  = 53.13˚ 15  9
1. Name the sides 15
Hyp
2. Choose the correct trig ration
Adj
Hyp
Cos  =
3. Enter the given data  9 15
Cos  = 9
Adj
4. Calculate the angle by using the “inverse ratio” button on the calculator. i.e. cos-1 9 15 
 = Cos-1
 = 53.13˚

20.  Opp Sin  = Hyp 9 Sin  = 15 9  = Sin-1 15  = 36.87˚ 15  9
1. Name the sides 15
Hyp 
2. Choose the correct trig ration
Opp
Hyp
Sin  =
3. Enter the given data 9 15
Sin  = 9
Opp
4. Calculate the angle by using the “inverse ratio” button on the calculator. i.e. sin-1 9 15 
 = Sin-1
 = 36.87˚

21. Opp Adj Opp Hyp Adj Hyp Tan  = Sin  = Cos  = Hypotenuse Opposite 
Adjacent
Opp
Adj
Opp
Hyp
Adj
Hyp
Tan  =
Sin  =
Cos  =