Make sure the calculator is in Degree Mode DRG button Practice getting the sinecostan of various angles Inverse functions 2 nd F button Use of backets is important when finding inverses ID: 749263
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Slide1
Junior Cert
TRIGONOMETRYSlide2
Make sure the calculator is in Degree Mode (DRG button)
Practice getting the sine/cos/tan of various anglesInverse functions: [2nd F button] Use of backets is important when finding inverses:e.g
2
Some considerationsSlide3
SECTION 1
RIGHT ANGLED TRIANGLESSlide4
RIGHT ANGLED TRIANGLES
HYPOTHENUSE
90
0
A
OPPOSITE
ADJACENT
HYPOTHENUSE
90
0
A
OPPOSITE
ADJACENTSlide5
a
b
c
a
2
+b
2
= c
2
PYTHAGORAS THEOREM
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).Slide6
Hypotenuse [H]Slide7
Hypotenuse [H]
A
Opposite [O]
Adjacent [A]Slide8
Hypotenuse [H]
A
Opposite [O]
Adjacent [A]Slide9
[H]
A
[O]
[A]
Cosine
Cos A =
A
H
Sine
Sin A =
O
H
Tangent
Tan A =
O
A
SOHCAHTOASlide10
[5]
[3]
[4]
A
SOHCAHTOA
[H]
[O]
[A]
Sin A =
O
H
=
3
5Slide11
[5]
A
[3]
[4]
SOHCAHTOA
[H]
[O]
[A]
Cos A =
A
H
=
4
5Slide12
[3]
SOHCAHTOA
[H]
[5]
A
[4]
[O]
[A]
Tan A =
O
A
=
3
4Slide13
[13]
A
[12]
[5]
SOHCAHTOA
[H]
[O]
[A]
Sin A =
O
H
=
12
13Slide14
[13]
A
[12]
[5]
SOHCAHTOA
[H]
[O]
[A]
Cos A =
A
H
=
5
13Slide15
[13]
A
[12]
[5]
SOHCAHTOA
[H]
[O]
[A]
Tan A =
O
A
=
12
5Slide16
[15]
30
0
x
SOHCAHTOA
[H]
[O]
[A]
Sin 30
0
=
O
H
=
x
15
Looking for x
O
Given
H
Sin 30
0
= 0.5
x
15
0.5
1
=
x
=
15(0.5)
= 7.5Slide17
[15]
50
0
x
SOHCAHTOA
[H]
[O]
[A]
tan 50
o
=
O
A
=
x
15
Looking for x
O
Given
A
Tan 50
o
= 1.1917
x
=
15(1.1918)
= 17.876
x
15
1.1917
1
=Slide18
[15]
35
o
16’
x
SOHCAHTOA
[H]
[O]
[A]
Cos 35
o
16’ =
A
H
=
15
x
Looking for x
H
Given
A
Cos 35
o
16’ = 0.8164
x(0.8165)
= 15
x =
15
x
0.8164
1
=
15
0.8165
= 18.37Slide19
THE ANGLE OF ELEVATION AND DEPRESSION
(b) Angle of elevation = Angle looking up
depression
elevation
(a) Angle of depression = Angle looking downSlide20
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.
20
0
100m
height
90
0
QUESTIONS ON RIGHT ANGLED TRIANGLESSlide21
20
0
100m
height
90
0
HYP
opp
In this we are given the
Hyp
. And we are looking for the
Opp
So we use the
Sin
FormulaSlide22
10m
14mSlide23
10m
8mSlide24
Note: If given ratio always draw right angled triangle
Adj = 5
Hyp = 13
x