1. Six Example with choice
SOH CAH TOA
Introduction
Sin
Side
Angle
Cos
Side
Angle
Side
Angle
Tan
SCT
Side
Angle
Six Example with choice

2. Find the angle           7 b° f° 4 New Ex B A O O C H T A S= = 7 = = b° f° = = = 4
sin
sin-1
cos-1
cos
tan-1
tan
SHIFT
Hyp
sin-1
cos-1
tan-1
Opp
(-) √ C x ÷ 5 6 7 8 9 + - On
Adj 1 2 3 4 . =
Clear
Ans
New Ex B

3. Find the Side           Hyp 13 b 61° e 11.37005619 New Ex AO A O H C H T A S       H O
Hyp =
SOH
Opp = 13 = b =
61° e = = =
sin-1
sin
cos-1
cos
13xSin 61
tan-1
tan
SHIFT
Hyp
tan-1
sin-1
cos-1
Opp
(-) √ C x ÷ 5 6 7 8 9 + - On
Adj
Sin 1 2 3 4 . =
Clear
Ans
New Ex A

4. 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 9° = … Sin 30° = Sin 83.7° = …
Height x°
The calculator also gives unique values for the Cos and Tan of an angle
Width
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
The next slide shows a RAT . You can enter a value into one of
Angle
Width
Height
then click Draw
Use the calculator to check that the Sine of Angle equals the height and Cos Angle equals the width

5. Enter a value for Angle/Width/Height then click Draw
1.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
Enter Sin 20 on calculator to get height of a triangle with angle 20°
sin-1
tan-1
cos-1
sin
sin-1
cos
cos-1
tan-1
tan
SHIFT
Ans On
(-) √ x ÷ 6 7 8 9
0.5 + -
Angle 30
Width
0.866
Height 1 2 3 4 5 = .
Cos C
Test
Draw

6. Hyp
Hyp 1
Sin 38° 4
=0.616
38°
Cos 38°
38°
=0.788 x x
Hyp
Hyp
New Angle
New Hypotenuse
Calculate

7. Definition Height Hyp ÷ ÷ Opp Sin x° Hyp Height x° = =Height÷Hyp
Adj
Hyp
Width
Width
=Width÷Hyp
Cos x° =
Cos x° x
Hyp
Hyp
Compare to DST triangle. Can get a definition for Sin and Cos for ALL triangles.

8. Applying Trig to all triangles
DEFINITIONS
Opp
Hyp =
Opp
Sin x°
Opp
Hyp =
Tan x°
Adj
Adj x° =
Cos x°
Hyp
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
In a RAT the longest side is the HYPotenuse
Hyp
Opp
Go across from the angle to find OPPosite x°
The Adjacent is between the marked Angle and the right Angle
Adj

9. What is SohCahToa Opp Sin x° Hyp = Soh
The next slides show you how to use SohCahToa
Sin , Cos and Tan MUST be followed by an angle
Adj =
Cah
Cos x°
Hyp
Opp
Tan x° =
Toa
Adj O A O S H C H T H

10. Using SohCahToa to find a side    O A O S H C H T A      
Hyp =
SOH
Opp = b
Opp 13
Sin
61° = = b 13
Hyp
61° b
13 x Sin 61 = =
11.37 =
Identify sides then click letters in SohCahToa
sin-1
cos-1
tan-1
cos-1
sin-1
tan-1
b on its own. Opposite of Div is mult

11. Using SohCahToa to find a side   O A O S H C H T A      
TOA =
Opp = e
Opp
Tan
51° = e = 12
Adj
51° e =
12 x Tan 51 =
14.819
Adj = 12
Identify sides then click letters in SohCahToa
sin-1
cos-1
tan-1
cos-1
sin-1
tan-1
Adj
51° No

12. Using SohCahToa to find an angle   O A O S H C H T A      
CAH
Hyp =
5 ÷9 = 5
Adj 9
Cos
0.556 c° = = 9
Hyp c° c° =
Cos-1 ( ) =
56.3
Adj = 5
Move Cos to other side --- > Cos-1
5÷9
sin
cos
tan
SHIFT
Ans
sin-1
cos-1
tan-1
sin-1
tan-1
cos-1
Ans
Opp
(-) √ C x ÷ 5 6 7 8 9 + - On No
Adj c° 1 2 3 4 . =
Ans

13.        a b c 18.71 d 5.23 e 6.89 f 13.16 7 -6 All Sin 14
9.37 
13° b 25 b a 80 18
22°      c
18.71 50 d d 6°
5.23
12° c e 90 f
6.89 f e
17°
13.16 45 7
16°
sin
sin-1
cos-1
cos
tan-1
tan -6
SHIFT
sin-1
tan-1
cos-1 25
(-) √ C x ÷
All Sin 14
Next Six
5.676 x 10 5 6 7 8 9 + - On
6 Sides 1 2 3 4 . = A
Ans

14. 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° = …. Sin 83.7° = …
The calculator can also give a value for each angle called the Cos and also the Tan
Cos 30° = …… Cos 9° = …. Cos 83.7° = …
Tan 30° = …… Tan 9° = …. Tan 83.7° = …
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