Super Trig PowerPoint Warm up Solve the following equations: 1)20= 2)15= 3)8= 4)7= 5)16= X2X2 X3X3 32 X 21 X 64 X.

Super Trig PowerPoint

Warm up Solve the following equations: 1)20= 2)15= 3)8= 4)7= 5)16= X2X2 X3X3 32 X 21 X 64 X

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

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

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

Labelling Right Angle Triangle 10 multiple choice questions

OppositeAdjacent Hypotenuse A)B) C) X What is the side marked with an X?

Adjacent HypotenuseOpposite A)B) C) X What is the side marked with an X?

HypotenuseOpposite Adjacent A)B) C) X What is the side marked with an X?

OppositeAdjacent Hypotenuse A)B) C) X What is the side marked with an X?

Hypotenuse AdjacentOpposite A)B) C) X What is the side marked with an X?

AdjacentOpposite Hypotenuse A)B) C) X What is the side marked with an X?

OppositeHypotenuse Adjacent A)B) C) X What is the side marked with an X?

Opposite HypotenuseAdjacent A)B) C) X What is the side marked with an X?

HypotenuseOpposite Adjacent A)B) C) X What is the side marked with an X?

Practice

Trigonometry-Day 2 Bell work: Copy and Complete: Identify the opposite side and adjacent side from: (a) Angle P(b) Angle R

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

SOHCAHTOA

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

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:

Practice some more Find tan A: 24.19 12 A 21 8 4 A 8 Find tan A:

Ex. 1: Finding Trig Ratios Fractions sin A = opposite hypotenuse cosA = adjacent hypotenuse tanA = opposite adjacent

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

Practice

Trigonometry-Day 3

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

Skiers On Holiday Can Always Have The Occasional Accident SOHCAHTOA Tan= Opposite Adjacent Cos= Adjacent Hypotenuse Sin= Opposite Hypotenuse

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.

SOHCAHTOA 7cm X 35 opposite Hypotenuse This question will use Sine Sin35= X7X7 Sin= OHOH

SOHCAHTOA X 8cm 17 opposite Adjacent This question will use Tan Tan17= 8X8X Tan= OAOA

SOHCAHTOA X 8cm 43 opposite Hypotenuse This question will use Sin Sin43= 8X8X Sin= OHOH

SOHCAHTOA X 8cm 26 Hypotenuse Adjacent This question will use Cosine cos26= X8X8 cos= AHAH

Sin, Cos or Tan? 10 multiple choice questions

SinCos Tan A)B) C) 35 X Will you use Sin, Cos or Tan with this question? 11cm

Cos SinTan A)B) C) 14 X Will you use Sin, Cos or Tan with this question? 15cm

SinCos Tan A)B) C) 40 X Will you use Sin, Cos or Tan with this question? 17cm

TanSin Cos A)B) C) 50 X Will you use Sin, Cos or Tan with this question? 5cm

Sin CosTan A)B) C) 51 X Will you use Sin, Cos or Tan with this question? 6cm

TanSin Cos A)B) C) 16 X Will you use Sin, Cos or Tan with this question? 8cm

CosSin Tan A)B) C) 42 14cm Will you use Sin, Cos or Tan with this question? X

TanCos Sin A)B) C) 35 X Will you use Sin, Cos or Tan with this question? 4cm

Sin CosTan A)B) C) 63 X Will you use Sin, Cos or Tan with this question? 3.4cm

SinTan Cos A)B) C) 71 X Will you use Sin, Cos or Tan with this question? 5mm

Practice

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

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

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

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

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)

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

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

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)

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

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

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)

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

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

Bell Work You have 10 minutes to complete yesterdays classwork. The trig tables are located on your desks. 10 minutes End

Trigonometry Day 5 Finding missing angles

Some Old Hairy Camels Are Hairier Than Other Animals SOHCAHTOA Tan= Opposite Adjacent Cos= Adjacent Hypotenuse Sin= Opposite Hypotenuse

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=

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)=

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=

Practice Questions 10cm 11cm 17cm 11cm 20cm 12cm 18cm 5cm15cm 23cm 35cm 22cm 10cm 12cm 6cm 13cm Answers : 1)50.2 2)28.6 3)59.1 4)52.3 5)63.4 6)65.4 7)28.6 8)40.9

Lets Review-Day 6 Write out the rule for Sine, Cosine and Tangent. Make up your own way of remembering SOHCAHTOA

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

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

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

Answers: 1)3.1cm 2)6.1cm 3)5.1cm 4)17.1cm 5)4.5cm 6)8.6cm 7)20.5cm 8)31.1cm 9)117.6cm 10)1.5cm 11)4.1cm 12)108.9cm Extra-Practice

Super Trig PowerPoint Warm up Solve the following equations: 1)20= 2)15= 3)8= 4)7= 5)16= X2X2 X3X3 32 X 21 X 64 X.

Documents

x slide

adjacent slide

tangent slide

practice slide

sohcahtoa slide

hypotenuseadjacent ab

angle pb angle r slide

sides hypotenuse