2.3 the sine and cosine ratios
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2.3 The Sine and Cosine Ratios
MFM2P
Back in the day….
Yesterday, we created 3 similar triangles…
A
F
E
G
B C D
20 units 10 units 10 units
1015
20
E
B
20
10
A A C
30
15
F
A
G
D
20
40
Neat Things about Ratios!!! Looking at Ratio 1
G
E
B
20
10
A A C
30
15
F
A
G
D
20
40
BE
AE 10 .
22.3
CF
AF 15 .
33.5
DG
AF 20 .
44.7
= 0.45 = 0.45= 0.45
When I look at the triangle from A OPPOSITE .
HYPOTENUSE0.45
OPP
ADJ A
HYP
22.333.5
44.7
The Sine Ratio!
When I look at the triangle from A OPPOSITE .
HYPOTENUSE0.45
There is a special name for this ratio. It is called the SINE RATIO. We can use it to solve for A.
OPP
ADJ A
HYP
OPPOSITE . HYPOTENUSESIN A =
The Sine Ratio!
If we know A, and one side, we can calculate the length of the other side.
OPP
ADJ A
HYP
OPPOSITE .
HYPOTENUSESIN A = 11
x
SIN 37° =11
x
C
B
11 cm
37°A
x
(11) SIN 37° = x
6.62 cm = x
Therefore the length of side BC is 6.6 cm
Looking at Ratio 2
G
E
B
20
10
A A C
30
15
F
A
G
D
20
40
AB
AE 20 .
22.3
AC
AF 30 .
33.5
AD
AF 40 .
44.7
= 0.90 = 0.90= 0.90
When I look at the triangle from A ADJACENT .
HYPOTENUSE0.90
Neat Things about Ratios!!! OPP
ADJ A
HYP
22.333.5
44.7
The COSINE Ratio!
When I look at the triangle from A ADJACENT .
HYPOTENUSE0.90
There is a special name for this ratio. It is called the COSINE RATIO. We can use it to solve for A
OPP
ADJ A
HYP
ADJACENT . HYPOTENUSECOS A =
The COSINE Ratio!
If we know A, and one side, we can calculate the length of the other side.
OPP
ADJ A
HYP
ADJACENT .
HYPOTENUSECOS A = 35
x
COS 50° =35
x
C
B
35 m
50°A x
(35) COS 50° = x
22.497 m = x
Therefore the length of side AB is 22.5 m
Using the Sides to Solve for A
If we know given the side length, we can use them to solve forA
A storm caused a 13.5m lamp post to lean over. The top of the pole is now 11.5m above the ground. Find the measure of the angle between the lamp
post and the ground, to the nearest degree
11.513.5m
13.5m
Finding the Measure of an Angle
13.5 m
11.5 m
x°
4.58
851851851.0sin
851851851.0 sin5.13
5.11 sin
sin
1
x
x
x
x
Hypotenuse
Oppositex
2nd Function sin-1 11.5 13.5( ) =
Are you confused?!?!
If your finding this frustrating… don’t worry
Its been the “COS” of frustration for many math students!
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