1. Junior Cert
TRIGONOMETRY

2. Some considerations
Make sure the calculator is in Degree Mode (DRG button)
Practice getting the sine/cos/tan of various angles
Inverse functions: [2nd F button] Use of backets is important when finding inverses: e.g
Some notes for each bullet in turn:
This is the first crucial step that has to be carried out before any trig work occurs
This is to enable pupils to get a ‘feel’ for using these new buttons
Explain that 2nd F button puts the calculator into inverse mode. So if we have a ratio, we must use 2nd F to find the angle.

3. SECTION 1
RIGHT ANGLED TRIANGLES

4. RIGHT ANGLED TRIANGLES
HYPOTHENUSE
HYPOTHENUSE
OPPOSITE
ADJACENT
900 A
900
ADJACENT
OPPOSITE

5. a2 +b2 = c2 PYTHAGORAS THEOREM c a b
The square of the hypotenuse is equal to the sum of the squares on the other 2 sides.
This theorem is used when you are looking for the length of one side of a triangle when you are given the measurements of the other 2 sides.
( Remember this theorem only works for right angled triangles).

6. Hypotenuse [H]

7. Hypotenuse [H]
Opposite [O] A
Adjacent [A]

8. A
Hypotenuse [H]
Adjacent [A]
Opposite [O]

9. SOHCAHTOA Cosine A Cos A = H [H] [O] Sine O Sin A = H A Tangent [A] O
Tan A =
SOHCAHTOA

10. [5]
[3]
[4]
[H]
[O] A
[A] O 3
SOHCAHTOA
Sin A = = H 5

11. [5] A
[3]
[4]
[H]
[O]
[A] A 4
SOHCAHTOA
Cos A = = H 5

12. [5] A
[4]
[O]
[H]
[3]
[A] O 3
SOHCAHTOA
Tan A = = A 4

13. [13] A
[12]
[5]
[H]
[O]
[A] O 12
SOHCAHTOA
Sin A = = H 13

14. [13] A
[12]
[5]
[H]
[O]
[A] A 5
SOHCAHTOA
Cos A = = H 13

15. [13] A
[12]
[5]
[H]
[O]
[A] O 12
SOHCAHTOA
Tan A = = A 5

16. O SOHCAHTOA H Looking for x [15] 300 x Given [H] [O] O x Sin 300 = = H
0.5 1 =
[A]
SOHCAHTOA x =
15(0.5)
= 7.5

17. SOHCAHTOA O A Looking for x [15] 500 x Given [H] [O] O x tan 50o = = A
1.1917 1 =
[A]
SOHCAHTOA x =
15(1.1918) =

18. SOHCAHTOA H A Looking for x [15] 35o 16’ x Given A 15 [H]
Cos 35o 16’ = =
[O] H x
Cos 35o 16’ = 15 x
0.8164 1 =
[A]
x(0.8165)
= 15
SOHCAHTOA 15
x =
= 18.37
0.8165

19. THE ANGLE OF ELEVATION AND DEPRESSION
(a) Angle of depression = Angle looking down
(b) Angle of elevation = Angle looking up
depression
elevation

20. QUESTIONS ON RIGHT ANGLED TRIANGLES
Example 1
A plane takes of at an angle of 200 to the level ground. After flying for 100m how high is it off the ground.
100m
height
900
200

21. 100m
HYP
opp
height
900
200
In this we are given the Hyp. And we are looking for the Opp
So we use the Sin Formula

22. 14m
10m

23. 10m 8m

24. Note: If given ratio always draw right angled triangle
Adj = 5
Hyp = 13 x