Transcript junior cert trigonometry revision notes




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
3
5
-1  3 
A  Sin  
5
If Sin A 
2
SECTION 1
RIGHT ANGLED TRIANGLES
RIGHT ANGLED TRIANGLES
A
A
ADJACENT
ADJACENT
900
900
PYTHAGORAS THEOREM
c
a
b
a2 +b2 = c2
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).
Hypotenuse [H]
Hypotenuse [H]
Opposite [O]
A
Adjacent [A]
A
Hypotenuse [H]
Adjacent [A]
Opposite [O]
Cosine
Cos A =
A
H
[O]
Sine
Sin A =
[H]
O
H
A
Tangent
Tan A =
[A]
O
A
SOHCAHTOA
[5]
[H]
[O] [3]
A
[4]
SOHCAHTOA
[A]
Sin A =
O
H
=
3
5
[5]
[H]
[O] [3]
A
[4]
SOHCAHTOA
[A]
Cos A =
A
H
=
4
5
[5]
[H]
[O] [3]
A
[4]
SOHCAHTOA
[A]
Tan A =
O
A
=
3
4
[13] [H]
[O] [12]
A
[5]
SOHCAHTOA
[A]
Sin A =
O
H
=
12
13
[13] [H]
[O] [12]
A
[5]
SOHCAHTOA
[A]
Cos A =
A
H
=
5
13
[13] [H]
[O] [12]
A
[5]
SOHCAHTOA
[A]
Tan A =
O
A
=
12
5
[O]
x
[15]
Looking for x
O
Given
H
[H]
Sin
300
O
=
=
H
Sin 300 = 0.5
300
[A]
SOHCAHTOA
x
15
x
=
0.5
1
= 15(0.5)
= 7.5
x
15
Looking for x
O
Given
A
[H]
[O]
x
tan
50o
O
=
A
=
x
15
Tan 50o = 1.1917
500
[15]
[A]
SOHCAHTOA
x
15
x
=
1.1917
1
= 15(1.1918)
= 17.876
x
[O]
[H]
Looking for x
H
Given
A
Cos
35o
A
16’ =
H
=
15
x
Cos 35o 16’ = 0.8164
15
35o 16’
[15]
[A]
SOHCAHTOA
x
=
x(0.8165)
x=
0.8164
1
= 15
15
0.8165
= 18.37
THE ANGLE OF ELEVATION AND DEPRESSION
(a) Angle of depression = Angle looking down
(b) Angle of elevation = Angle looking up
depression
elevation
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
200
900
100m
900
200
In this we are given the Hyp. And we are looking for the Opp
So we use the Sin Formula
Opp
h
Sin 20 

Hyp 100
h
 0 .342 
100
Sin20  0.3420
h  34.2m
Example 2. A building 14m heigh casts a shadow 10m in length
Find the angle of elevation of the sun.
14m
x
10m
Opp
Tan x 
Adj
14
Tan x  
 1.4
10
x  5428'
Example 3. A ladder 10m long just reaches the top of a wall 8m high.
Find the angle between the ladder and the wall.
8m

10m
Adj
Cos 
Hyp
Cos  
8
 .8
10
  36 53'
5
Example 4. If Cos  , find Sin and Tan 2 , 0    90
13
without using calculator.
Note: If given ratio always draw right angled triangle
x

Adj = 5
Adj 5
Cos 

Hyp 13
By Pythagoras 13 2  x 2  5 2
 x  12 (Note triplet)
Opp 12
Sin 

Hyp 13
2
144
 Opp   12 
2
2
   
Tan   (Tan )  
25
 Adj   5 
2