soh cah toa sin cos tan side angle side angle side angle sct side angle six example with choice...
TRANSCRIPT
![Page 1: SOH CAH TOA Sin Cos Tan Side Angle Side Angle Side Angle SCT Side Angle Six Example with choice Introduction](https://reader033.vdocuments.mx/reader033/viewer/2022061607/56649dc45503460f94ab7ccb/html5/thumbnails/1.jpg)
SOH CAH TOA
Sin
Cos
Tan
Side Angle
Side Angle
Side Angle
SCT Side Angle
Six Example with choice
Introduction
![Page 2: SOH CAH TOA Sin Cos Tan Side Angle Side Angle Side Angle SCT Side Angle Six Example with choice Introduction](https://reader033.vdocuments.mx/reader033/viewer/2022061607/56649dc45503460f94ab7ccb/html5/thumbnails/2.jpg)
0 1 2 3 4
5 6 7 8 9
C
.
÷x0 + On
²
-
Ans
=
√(-)
sin cos tan SHIFTHyp
Opp
Adj
Clear
Find the angle
b°b°
S H
O
C H
A
T A
O
= 4
=
7
=
=
=f° =
=
BNew Ex
![Page 3: SOH CAH TOA Sin Cos Tan Side Angle Side Angle Side Angle SCT Side Angle Six Example with choice Introduction](https://reader033.vdocuments.mx/reader033/viewer/2022061607/56649dc45503460f94ab7ccb/html5/thumbnails/3.jpg)
0 1 2 3 4
5 6 7 8 9
13xSin 61
C
.
÷x11.3700561
9+ On
²
-
Ans
=
√(-)
sin cos tan SHIFT
Sin
Hyp
Opp
Adj
Clear
Find the Side
61°61°
Hyp Opp
S H
O
C H
A
T A
O
=
=
b13
=
=
=e =
SOH H O
=
ANew Ex
![Page 4: SOH CAH TOA Sin Cos Tan Side Angle Side Angle Side Angle SCT Side Angle Six Example with choice Introduction](https://reader033.vdocuments.mx/reader033/viewer/2022061607/56649dc45503460f94ab7ccb/html5/thumbnails/4.jpg)
Trigonometry and the Right Angle Triangle
x°
WidthH
eig
ht
For every angle less than 90° a calculator can be used to find a unique value called its Sine
Sin 9° = 0.1564… Sin 30° =0.5 Sin 83.7° = 0.1564…The calculator also gives unique values for the Cos and Tan of an angle
In a RAT with a hypotenuse ( longest side ) of length 1 and an angle of 25° then
The Sin 25° is the height, the Cos 25° is the width and the Tan 25° is a measure of how steep the hypotenuse is
Angle Width Height
The next slide shows a RAT . You can enter a value into one of
then click Draw
Use the calculator to check that the Sine of Angle equals the height and Cos Angle equals the width
![Page 5: SOH CAH TOA Sin Cos Tan Side Angle Side Angle Side Angle SCT Side Angle Six Example with choice Introduction](https://reader033.vdocuments.mx/reader033/viewer/2022061607/56649dc45503460f94ab7ccb/html5/thumbnails/5.jpg)
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0.55
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0.85
0.90
0.95
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0.95
1.00
Test
Angle 30 Width Height0.866
0.5
Draw0
1 2 3 4 5
6 7 8 9
C.
÷x
0
+
On
²
-
Ans
=
√(-)
sin cos tan
SHIFT
Cos
Enter a value for Angle/Width/Height then click Draw
Enter Sin 20 on calculator to get height of a triangle with angle 20°
![Page 6: SOH CAH TOA Sin Cos Tan Side Angle Side Angle Side Angle SCT Side Angle Six Example with choice Introduction](https://reader033.vdocuments.mx/reader033/viewer/2022061607/56649dc45503460f94ab7ccb/html5/thumbnails/6.jpg)
38°
=0.788
=0.616
38°
14
Sin 38°
Cos 38°
HypHyp
x
Hypx
Hyp
New Hypotenuse
New Angle
Calculate
![Page 7: SOH CAH TOA Sin Cos Tan Side Angle Side Angle Side Angle SCT Side Angle Six Example with choice Introduction](https://reader033.vdocuments.mx/reader033/viewer/2022061607/56649dc45503460f94ab7ccb/html5/thumbnails/7.jpg)
Definition
Height
Sin x°
Hyp
÷
Width
Cos x° Hypx
x°
Hy
pOpp
Adj
÷
Sin x° =
Height
Hyp
=Height÷Hyp
Width
HypCos x° = =Width÷Hy
p
Compare to DST triangle. Can get a definition for Sin and Cos for ALL triangles.
![Page 8: SOH CAH TOA Sin Cos Tan Side Angle Side Angle Side Angle SCT Side Angle Six Example with choice Introduction](https://reader033.vdocuments.mx/reader033/viewer/2022061607/56649dc45503460f94ab7ccb/html5/thumbnails/8.jpg)
Applying Trig to all triangles
x°
In a RAT the longest side is the HYPotenuse
Hy
pHy
p
x°
Go across from the angle to find OPPosite
Opp
Opp
The Adjacent is between the marked Angle and the right Angle
Adj
Adj
Sin x°
DEFINITIONS
Opp
Hyp=
Cos x°
Adj
Hyp=
Tan x°
Opp
Adj=
You can use the above definitions to work out an angle in a RAT if you know two sides
or
You can work out a side if you know an angle and one of the remaining sides
![Page 9: SOH CAH TOA Sin Cos Tan Side Angle Side Angle Side Angle SCT Side Angle Six Example with choice Introduction](https://reader033.vdocuments.mx/reader033/viewer/2022061607/56649dc45503460f94ab7ccb/html5/thumbnails/9.jpg)
What is SohCahToa
Sin x°
Opp
Hyp=
Cos x°
Adj
Hyp=
Tan x°
Opp
Adj=
Soh
S
O
H C
A
H T
O
H
Cah
Toa
The next slides show you how to use SohCahToa
Sin , Cos and Tan MUST be followed by an angle
![Page 10: SOH CAH TOA Sin Cos Tan Side Angle Side Angle Side Angle SCT Side Angle Six Example with choice Introduction](https://reader033.vdocuments.mx/reader033/viewer/2022061607/56649dc45503460f94ab7ccb/html5/thumbnails/10.jpg)
Using SohCahToa to find a side
61°61°
Hyp Opp
S H
O
C H
A
T A
O
=
=
b13
=
Sin 61°
=b
13
OppHyp
13 x Sin 61 = 11.37b =
SOH
=
b on its own. Opposite of Div is mult
Identify sides then click letters in SohCahToa
![Page 11: SOH CAH TOA Sin Cos Tan Side Angle Side Angle Side Angle SCT Side Angle Six Example with choice Introduction](https://reader033.vdocuments.mx/reader033/viewer/2022061607/56649dc45503460f94ab7ccb/html5/thumbnails/11.jpg)
Using SohCahToa to find a side
51°51°
Opp
S H
O
C H
A
T A
O
= 12
=
e
=
Tan 51°
=e
12
OppAdj
12 x Tan 51 = 14.819e =
TOA
=
AdjIdentify sides then click letters in SohCahToa
No 51°51° AdjAdj
![Page 12: SOH CAH TOA Sin Cos Tan Side Angle Side Angle Side Angle SCT Side Angle Six Example with choice Introduction](https://reader033.vdocuments.mx/reader033/viewer/2022061607/56649dc45503460f94ab7ccb/html5/thumbnails/12.jpg)
Using SohCahToa to find an angle
0 1 2 3 4
5 6 7 8 9
Ans
C
.
÷x0.55555556 + On
²
-
Ans
=
√(-)
sin cos tan SHIFTOpp
c°c°
Hyp
S H
O
C H
A
T A
O
= 5
=
9
=
Cos c° =5
9
Adj
Hyp
Cos-1 (0.55556...) = 56.3c° =
CAH
= 0.556
Adj
No
c°c° AdjAdj
5 ÷9
Move Cos to other side --- > Cos-1
Ans
56.2510114
5÷9
![Page 13: SOH CAH TOA Sin Cos Tan Side Angle Side Angle Side Angle SCT Side Angle Six Example with choice Introduction](https://reader033.vdocuments.mx/reader033/viewer/2022061607/56649dc45503460f94ab7ccb/html5/thumbnails/13.jpg)
0 1 2 3 4
5 6 7 8 9
C
.
÷x0 + On
²
-
Ans
=
√(-)
sin cos tan SHIFT
22°
a25
18.71
5.23
6.89
13.16
13°
80
12°c
2516°
e
50
45
17°
f
d
90
6°
a9.37
b18
c
d
e
f
Next Six
b
All Sin
6 SidesA
![Page 14: SOH CAH TOA Sin Cos Tan Side Angle Side Angle Side Angle SCT Side Angle Six Example with choice Introduction](https://reader033.vdocuments.mx/reader033/viewer/2022061607/56649dc45503460f94ab7ccb/html5/thumbnails/14.jpg)
Trigonometry and the Right Angle Triangle
For every angle less than 90° a calculator can be used to find a unique value called its Sine …..
Sin 30° = 0.5 Sin 9° = 0.1564…. Sin 83.7° = 0.1564…
The calculator can also give a value for each angle called the Cos and also the Tan
Cos 30° = 0.8660…… Cos 9° = 0.98768…. Cos 83.7° = 0.1097…
Tan 30° = 0.5773…… Tan 9° = 0.1583…. Tan 83.7° = 9.0578…In a RAT with a hypotenuse ( longest side ) of length 1 and an angle of 25° then
The Sin 25° is the height, the Cos 25° is the width and the Tan 25° is a measure of how steep the hypotenuse is