Warm up Solve the following equations: 1)20= 2)15= 3)8= 4)7=
5)16= X2X2 X3X3 32 X 21 X 64 X
Slide 5
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
Slide 6
Labelling the sides Hypotenuse 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
Slide 7
Labelling the sides Opposite What we call the other two sides
will change depending on which angle we are working with, for
example.. 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
Adjacent
Slide 8
Labelling Right Angle Triangle 10 multiple choice
questions
Slide 9
OppositeAdjacent Hypotenuse A)B) C) X What is the side marked
with an X?
Slide 10
Adjacent HypotenuseOpposite A)B) C) X What is the side marked
with an X?
Slide 11
HypotenuseOpposite Adjacent A)B) C) X What is the side marked
with an X?
Slide 12
OppositeAdjacent Hypotenuse A)B) C) X What is the side marked
with an X?
Slide 13
Hypotenuse AdjacentOpposite A)B) C) X What is the side marked
with an X?
Slide 14
AdjacentOpposite Hypotenuse A)B) C) X What is the side marked
with an X?
Slide 15
AdjacentOpposite Hypotenuse A)B) C) X What is the side marked
with an X?
Slide 16
OppositeHypotenuse Adjacent A)B) C) X What is the side marked
with an X?
Slide 17
Opposite HypotenuseAdjacent A)B) C) X What is the side marked
with an X?
Slide 18
HypotenuseOpposite Adjacent A)B) C) X What is the side marked
with an X?
Slide 19
Practice
Slide 20
Trigonometry-Day 2 Bell work: Copy and Complete: Identify the
opposite side and adjacent side from: (a) Angle P(b) Angle R
Slide 21
Trigonometry-Rev. 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
by practicing writing the ratios for Sine, Cosine and Tangent
Slide 22
SOHCAHTOA
Slide 23
Trigonometric Ratios Name say SineCosinetangent Abbreviation
Abbrev. SinCosTan Ratio of an angle measure Sin = opposite side
hypotenuse cos = adjacent side hypotenuse tan =opposite side
adjacent side
Slide 24
Lets practice B c a C b A Write the ratio for sin A Write the
ratio for cos A Write the ratio for tan A Lets switch angles: Find
the sin, cos and tan for Angle B:
Slide 25
Practice some more Find tan A: 24.19 12 A 21 8 4 A 8 Find tan
A:
Slide 26
Ex. 1: Finding Trig Ratios Fractions sin A = opposite
hypotenuse cosA = adjacent hypotenuse tanA = opposite adjacent
Slide 27
Ex. 2: Finding Trig RatiosFind the sine, the cosine, and the
tangent of the indicated angle. Angle R Sin R = opposite hypotenuse
cosR = adjacent hypotenuse tanR = opposite adjacent
Slide 28
Practice
Slide 29
Trigonometry-Day 3
Slide 30
BELL WORK With your partner, identify each of the following:
hypotenuse: _______ side opposite angle A: _______ side adjacent to
angle A: _______ side opposite angle B: _______ side adjacent to
angle B: _______ A B C b a c c a b b a
Slide 31
Skiers On Holiday Can Always Have The Occasional Accident
SOHCAHTOA Tan= Opposite Adjacent Cos= Adjacent Hypotenuse Sin=
Opposite Hypotenuse
Slide 32
Our aim today We have looked at the three rules and have
practised labelling triangles. Today we will have to decide whether
we are using Sin, Cos or Tan when answering questions.
Slide 33
SOHCAHTOA 7cm X 35 opposite Hypotenuse This question will use
Sine Sin35= X7X7 Sin= OHOH
Slide 34
SOHCAHTOA X 8cm 17 opposite Adjacent This question will use Tan
Tan17= 8X8X Tan= OAOA
Slide 35
SOHCAHTOA X 8cm 43 opposite Hypotenuse This question will use
Sin Sin43= 8X8X Sin= OHOH
Slide 36
SOHCAHTOA X 8cm 26 Hypotenuse Adjacent This question will use
Cosine cos26= X8X8 cos= AHAH
Slide 37
Sin, Cos or Tan? 10 multiple choice questions
Slide 38
SinCos Tan A)B) C) 35 X Will you use Sin, Cos or Tan with this
question? 11cm
Slide 39
Cos SinTan A)B) C) 14 X Will you use Sin, Cos or Tan with this
question? 15cm
Slide 40
SinCos Tan A)B) C) 40 X Will you use Sin, Cos or Tan with this
question? 17cm
Slide 41
TanSin Cos A)B) C) 50 X Will you use Sin, Cos or Tan with this
question? 5cm
Slide 42
Sin CosTan A)B) C) 51 X Will you use Sin, Cos or Tan with this
question? 6cm
Slide 43
TanSin Cos A)B) C) 16 X Will you use Sin, Cos or Tan with this
question? 8cm
Slide 44
CosSin Tan A)B) C) 42 14cm Will you use Sin, Cos or Tan with
this question? X
Slide 45
TanCos Sin A)B) C) 35 X Will you use Sin, Cos or Tan with this
question? 4cm
Slide 46
Sin CosTan A)B) C) 63 X Will you use Sin, Cos or Tan with this
question? 3.4cm
Slide 47
SinTan Cos A)B) C) 71 X Will you use Sin, Cos or Tan with this
question? 5mm
Slide 48
Practice
Slide 49
Bell Work: Copy and complete 1)Late work is to be turned into
the __________________located___ _________. 2)Class work that is
due at the end of the period is turned into the ________________.
3)I need to bring to class a ___________, ____________ and a good
______________ 3 minutes
Slide 50
Trigonometry-Day 4 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
by practicing writing the ratios for Sine, Cosine and Tangent
Slide 51
Sine (sin) 30 5cm 10cm We use Sine when we have the Opposite
length and the Hypotenuse Try entering sin30 in your calculator, it
should give the same answer as 5 10 Sin30= 5 10 The rule we use is:
Sin= Opposite Hypotenuse
Slide 52
Sin Example 1 42 F 7cm We can use Sin as the question involves
the Opposite length and the Hypotenuse Sin42= F7F7 The rule we use
is: Sin= Opposite Hypotenuse 7 (Sin42)= F 4.68 cm (2dp)= F
Slide 53
Sin Example 2 17 10cm H We can use Sin as the question involves
the Opposite length and the Hypotenuse Sin17= 10 H The rule we use
is: Sin= Opposite Hypotenuse H x Sin17= 10 H= 10 Sin17 H= 34.2 cm
(1dp)
Slide 54
Cosine (cos) 50 Adjacent Hypotenuse We use cosine when we have
the Adjacent length and the Hypotenuse The rule we use is: Cos=
Adjacent Hypotenuse
Slide 55
Cos Example 1 53 A 9cm We can use Cos as the question involves
the Adjacent length and the Hypotenuse Cos53= A9A9 The rule we use
is: Cos= Adjacent Hypotenuse 9 x Cos53= A 5.42 cm (2dp)= A
Slide 56
Cos Example 2 17 9cm H We can use Cos as the question involves
the Adjacent length and the Hypotenuse Cos17= 9H9H The rule we use
is: Cos= Adjacent Hypotenuse H x Cos17= 10 H= 9 Cos17 H= 9.41 cm
(2dp)
Slide 57
Tangent (tan) 50 6.4cm (1dp) 10cm We use tangent when we have
the Opposite and Adjacent lengths. The rule we use is: Tan=
Opposite Adjacent
Slide 58
Tan Example 1 53 O 11cm We can use Tan as the question involves
the Adjacent and Opposite lengths Tan53= O 11 The rule we use is:
Tan= Opposite Adjacent 11 x Tan53= O 14.6 cm (1dp)= O
Slide 59
Tan Example 2 35 A 21cm We can use Tan as the question involves
the Adjacent and Opposite lengths Tan35= 21 A The rule we use is:
Tan= Opposite Adjacent A x Tan35= 21 A= 21 Tan35 A= 29.99 cm
(2dp)
Slide 60
The three rules So we have: Tan= Opposite Adjacent Cos=
Adjacent Hypotenuse Sin= Opposite Hypotenuse Sin=Tan= OAOA Cos=
AHAH OHOH SOHCAHTOA There are a few ways to remember this
Slide 61
Practice 1.Use Sine to find the missing lengths on these
triangles: 2. Use Cosine to find the missing lengths on these
triangles: 3.Use Tangent to find the missing lengths on these
triangles: O 15cm 50 17cm H 60 A 22cm 38 25cm H 60 O 15cm 42 11cm A
60 Tan= Opposite Adjacent Cos= Adjacent Hypotenuse Sin= Opposite
Hypotenuse
Slide 62
Bell Work You have 10 minutes to complete yesterdays classwork.
The trig tables are located on your desks. 10 minutes End
Slide 63
Trigonometry Day 5 Finding missing angles
Slide 64
Some Old Hairy Camels Are Hairier Than Other Animals SOHCAHTOA
Tan= Opposite Adjacent Cos= Adjacent Hypotenuse Sin= Opposite
Hypotenuse
Slide 65
SOHCAHTOA 7cm 3cm opposite Hypotenuse This question will use
Sin Sin= 3737 OHOH Find the missing angle Sin=0.42857... What angle
would give us this answer? Sin -1 0.42857...= 25.4 (1dp)= You could
use the ANS button on your calculator Sin -1 ANS=
Slide 66
SOHCAHTOA 8cm 6cm Adjacent Opposite This question will use Tan
Tan= 8686 OAOA Find the missing angle Tan=1.25 What angle would
give us this answer? Tan -1 1.25= 51.3 (1dp)=
Slide 67
SOHCAHTOA 12cm 9cm Adjacent Hypotenuse This question will use
Cos Cos= 9 12 Cos= AHAH Find the missing angle Cos=0.75 What angle
would give us this answer? Cos -1 0.75= 41.4 (1dp)= You could use
the ANS button on your calculator Cos -1 ANS=
Lets Review-Day 6 Write out the rule for Sine, Cosine and
Tangent. Make up your own way of remembering SOHCAHTOA
Slide 70
Find the missing lengths and angles X 16cm 30 1 14cm X 51 2
15cm 17cm 3 8cm 12cm 4 19cm 36cm 5 X 18cm 63 6 9cm 8.3cm 7 11.2cm X
35 8 X 15cm 43 9 X 23cm 50 10 40cm 53cm X 46cm 28 16cm 32cm X 36cm
18 61cm74cm 81cm 106cm 1112 16 15 1413 Answers: 1)8cm 2)22.2cm
3)48.6 4) 41.8 5)58.1 6)16cm 7)42.7 8)19.5cm 9)11cm 10)19.3 11)41
12)21.6cm 13)60 14)11.7cm 15)55.5 16)49.8
Slide 71
a b c d e f gh i 10cm 30 40 50 35 4542 27 38 51 Use sin, cos
and tan to find the missing lengths, round them to 1 d.p, and use
that answer to work out the next length. SideLength (rounded to 1
dp) a b c d e f g h i
Slide 72
a b c d e f gh i 10cm 30 40 50 35 4542 27 38 51 Use sin, cos
and tan to find the missing lengths, round them to 1 d.p, and use
that answer to work out the next length. SideLength (rounded to 1
dp) a b c d e f g h i SideLength (rounded to 1 dp) a 5 b 4.2 c 3.2
d 2.2 e 3.1 f 3.4 g 1.7 h 2.8 i 9.5