SOH CAH TOA

Sin

Cos

Tan

Side Angle

Side Angle

Side Angle

SCT Side Angle

Six Example with choice

Introduction

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

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

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

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

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

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°

38°

=0.788

=0.616

38°

14

Sin 38°

Cos 38°

HypHyp

x

Hypx

Hyp

New Hypotenuse

New Angle

Calculate

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.

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

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

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

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

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

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

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