eol: trigonometry … · trigonometry vocabulary: right angle triangle, hypotenuse, opposite side,...

Trigonometry

Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle

EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%

LO: Students will solveproblems that involve Trigonometry Ratios

Agenda:

1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure

TrigonometryApplication Math 2

Trigonometry



LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios

Agenda:


Trigonometry




Agenda:


Trigonometry

• We can use trigonometry to find missing angles and lengths of triangles.

• Trigonometry uses three functions, these are called:• Sine (shortened to Sin and pronounced “sign”)

• Cosine (shortened to Cos)

• Tangent (shortened to Tan)

• We will start working with right angled triangles

Trigonometry




Agenda:


Trigonometry




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Labelling the sides

The longest side, the one opposite the

right angle is called the hypotenuse

Before we can use Sin, Cos and Tan we need to be able to label the sides of a right angled

triangle

Trigonometry

Labelling the sides

Op

po

site

The name of the other two sides will change depending on

which angle we are working with, for example..

ϴ

Adjacent

If we are given (or need to work out) this

angle, we label the other sides like this..

But if we are

working with this

angle, we label the

sides like this...

Opposite

Ad

jace

nt

Trigonometry

OppositeAdjacent

Hypotenuse

A) B)

C)

ϴX

What is the side marked with an X?

Trigonometry

Adjacent

Hypotenuse OppositeA) B)

C)

ϴ

X


Trigonometry

Hypotenuse Opposite

Adjacent

A) B)

C)

ϴ

X


Trigonometry

Opposite Adjacent

Hypotenuse

A) B)

C)

ϴ

X


Trigonometry

Hypotenuse

Adjacent OppositeA) B)

C)

ϴX


Trigonometry

AdjacentOpposite

Hypotenuse

A) B)

C)

ϴX


Trigonometry

AdjacentOpposite

Hypotenuse

A) B)

C)

ϴ

X


Trigonometry

Opposite Hypotenuse

Adjacent

A) B)

C)

ϴ


Trigonometry

Opposite

Hypotenuse AdjacentA) B)

C)

ϴ

X


Trigonometry

Hypotenuse Opposite

Adjacent

A) B)

C)

ϴ

X


Trigonometry




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Trigonometry




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Sine (sin)

𝜃˚O

pp

osi

te

We use Sine ratio when we have the Oppositelength and the Hypotenuse

The Ratio we use is:

Sin𝜃 =𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒

ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

Trigonometry




Agenda:


Trigonometry




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Sin Example 1

42˚𝑥

We can use Sin as the question involves the Opposite length and the Hypotenuse




Sin42° =𝑥

7

7 x Sin42° = 𝑥

4.68𝑐𝑚 (2. 𝑑𝑝) = 𝑥

Trigonometry




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Trigonometry




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Sin Example 1

17˚

10𝑐𝑚

We can use Sin as the question involves the Opposite length and the Hypotenuse




Sin17° =10

𝑥

𝑥Sin17° = 10

𝑥 =34.2 ( 1 dp)

𝑥 =10

𝑆𝑖𝑛17

Trigonometry




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Trigonometry




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Cosine (cos)

𝜃 ˚

Adjacent

We use cosine when we have the Adjacentlength and the Hypotenuse


𝐶𝑜𝑠𝜃 =𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡


Trigonometry




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Trigonometry




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Cosine Example 1

53˚

𝑥

We can use Cosine as the question involves the Adjacent length and the Hypotenuse


Cos53° =𝑥

9

9 x Cos53° = 𝑥

5.42𝑐𝑚(2 𝑑𝑝) = 𝑥



Trigonometry




Agenda:


Trigonometry




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Cosine Example 2

We can use Cosine as the question involves the Adjacent length and the Hypotenuse


Cos26° =8

𝑥

𝑥Cos26° = 8

𝑥 = 8.9 ( 1 dp)𝑥 =

8

𝐶𝑜𝑠26



26˚

8 c

m

x

Trigonometry




Agenda:


Trigonometry




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Tangent (tan)

𝜃˚

AdjacentO

pp

osi

te

We use Tangent when we have the Oppositelength and the Adjacent


Tan𝜃 =𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒

𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡

Trigonometry




Agenda:


Trigonometry




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Tangent Example 1

We can use Tangent as the question involves the Adjacent length and the Opposite


Tan 53° =𝑥

11

11 x Tan53° = 𝑥

14.6𝑐𝑚(1 𝑑𝑝) = 𝑥

53˚

11𝑐𝑚𝑥



Trigonometry




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Trigonometry




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Tangent Example 2

We can use Tangent as the question involves the Adjacent length and the Opposite


Tan35° =21

𝑥

𝑥Tan35° = 21

𝑥 = 30cm ( 1 dp)𝑥 =

21

𝑇𝑎𝑛35



35˚

x2

1cm

Trigonometry




Agenda:


Trigonometry




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Sin𝜃 =𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒

𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

Tan𝜃 =𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒

𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡

𝑪𝑜𝑠𝜃 =𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡


SOH

CAH

TOA

Trigonometry Ratio

Trigonometry




Agenda:


Trigonometry




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Selecting Ratio

10cm

63o

x

sinѲ =

sin63 =

x = 10sin63

x = 8.91cm (2dp)

OppositeHypotenuse

x10

S O H

C A H

T 0 A

Trigonometry




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Trigonometry




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9cm

49o

x

CosѲ =

Cos49 =

x = 9cos49

x = 5.90 cm (2dp)

AdjacentHypotenuse

x9

S O H

C A H

T 0 A

Selecting Ratio

Trigonometry




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Trigonometry




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12cm

52o

x

TanѲ =

Tan52 =

x = 12Tan52

x = 15.26 cm (2dp)

OpppositeAdjacent

x12

S O H

C A H

T 0 A

Selecting Ratio

Trigonometry




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Trigonometry




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Determine the value of the unknown

x

7cm

35o

SOH CAH TOA

x = 4.90 cm (3 s.f.)

Trigonometry




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Trigonometry




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10cm

40o

SOH CAH TOA


p = 15.6 cm (3 s.f.)

Trigonometry




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Trigonometry




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20cm

35o

SOH CAH TOA


w = 24.4 cm (3 s.f.)

Trigonometry




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Trigonometry




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9 cm

y47o


y = 6.14 cm (3 s.f.)

Trigonometry




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Trigonometry




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z

13

55o

SOH CAH TOA


Z = 9.10 cm (3 s.f.)

Trigonometry

Finding Missing Angle - Sine

ϴ

4cm

Trig. Ratios can be used to find missing angle(ϴ)

Sin𝜃 =𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒


Sin𝜃 =𝟒

𝟓

Sin𝜃 = 0.800 (3 𝑠𝑓)

Sin𝜃 = 0.800 (3 𝑠𝑓)

𝜃 = 𝑆𝑖𝑛−1(0.800

𝜃 = 53.1°

Trigonometry

Finding Missing Angle - Cos


Cos𝜃 =𝑨𝑑𝑎𝑐𝑒𝑛𝑡


Cos𝜃 =3

𝟓

Cos𝜃 = 0.600 (3 𝑠𝑓)

Cos𝜃 = 0.600 (3 𝑠𝑓)

𝜃 = 𝐶𝑜𝑠−1(0.600

𝜃 = 53.1°

ϴ3cm

Trigonometry

Finding Missing Angle - Tan



𝑨𝑑𝑎𝑐𝑒𝑛𝑡

Tan𝜃 =4

3

𝜃 = 𝑇𝑎𝑛−1(4

3)

𝜃 = 53.1°

ϴ

4cm

3cm

Trigonometry

Trig Ratios

Sine Ratio:

SinѲ =

Cosine Ratio:

CosѲ =

Tangent Ratio:

TanѲ = Opposite

HypotenuseAdjacent

HypotenuseOppositeAdjacent

Hypotenuse

Opposite

Hypotenuse

Adjacent

Ad

jace

nt

Opposite

SOH CAH TOA

Trigonometry

Trigonometry

17cma cm

27o

Ѳ

15cm

9cm

11m38o

b m

10cm

14cm

𝜃

c cm

21cm

71𝑜

d cm

11cm

84𝑜

eol: trigonometry … · trigonometry vocabulary: right angle triangle, hypotenuse, opposite side,...

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