Super Trig PowerPoint

Warm up Solve the following equations: 8= 20= 7= 15= 16= 32 X X 2 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 Before we can use Sin, Cos and Tan we need to be able to label the sides of a right angled triangle The longest side, the one opposite the right angle is called the hypotenuse Hypotenuse

But if we are working with this angle, we label the sides like this... Labelling the sides What we call the other two sides will change depending on which angle we are working with, for example.. If we are given (or need to work out) this angle, we label the other sides like this.. Adjacent Opposite But if we are working with this angle, we label the sides like this... ϴ Opposite Adjacent

Labelling Right Angle Triangle 10 multiple choice questions

X A) B) C) What is the side marked with an X? ϴ Adjacent Opposite Hypotenuse C)

X A) B) C) What is the side marked with an X? ϴ Hypotenuse Opposite Adjacent C)

X A) B) C) What is the side marked with an X? ϴ Hypotenuse Opposite Adjacent C)

X A) B) C) What is the side marked with an X? ϴ Opposite Adjacent Hypotenuse C)

X A) B) C) What is the side marked with an X? ϴ Adjacent Opposite Hypotenuse C)

X A) B) C) What is the side marked with an X? ϴ Opposite Adjacent Hypotenuse C)

X A) B) C) What is the side marked with an X? ϴ Opposite Adjacent Hypotenuse C)

X A) B) C) What is the side marked with an X? ϴ Opposite Hypotenuse Adjacent C)

X A) B) C) What is the side marked with an X? ϴ Hypotenuse Adjacent Opposite C)

X A) B) C) What is the side marked with an X? ϴ Hypotenuse Opposite Adjacent C)

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 Sine Cosine tangent Sin Cos Tan Name “say” Sine Cosine tangent Abbreviation Abbrev. Sin Cos Tan Ratio of an angle measure Sinθ = opposite side hypotenuse cosθ = adjacent side tanθ =opposite side adjacent side

Let’s 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 B c a C b A Let’s 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 Find tan A: 8

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

Ex. 2: Finding Trig Ratios—Find the sine, the cosine, and the tangent of the indicated angle. Angle R opposite Sin R = hypotenuse adjacent cosR = hypotenuse opposite tanR = adjacent

Practice

Trigonometry-Day 3

With your partner, identify each of the following: 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: _______ c A B C b a c b b a a

Skiers On Holiday Can Always Have The Occasional Accident SOHCAHTOA Opposite Hypotenuse Adjacent Hypotenuse Opposite Adjacent Sinϴ= Cosϴ= Tanϴ=

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.

This question will use Sine SOH CAH TOA This question will use Sine O H Sinϴ= 7cm X Sin35= X 7 Hypotenuse opposite 35˚

This question will use Tan SOH CAH TOA This question will use Tan O A Tanϴ= Adjacent 17˚ 8 X Tan17= X 8cm opposite

This question will use Sin SOH CAH TOA This question will use Sin O H Sinϴ= X 43˚ 8 X Sin43= Hypotenuse 8cm opposite

This question will use Cosine SOH CAH TOA This question will use Cosine A H cosϴ= Adjacent 26˚ X 8 Hypotenuse cos26= 8cm X

10 multiple choice questions Sin, Cos or Tan? 10 multiple choice questions

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

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

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

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

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

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

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

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

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

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

Practice

Bell Work: Copy and complete Late work is to be turned into the __________________located____________. Class work that is due at the end of the period is turned into the ________________. 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) 10cm 5cm Opposite Sinϴ= Hypotenuse 5 Sin30= 10 30˚ We use Sine when we have the Opposite length and the Hypotenuse 5cm The rule we use is: Opposite Hypotenuse Sinϴ= Try entering sin30 in your calculator, it should give the same answer as 5 ÷ 10 5 10 Sin30=

Sin Example 1 7cm F Opposite Sinϴ= Hypotenuse F Sin42= 7 7 (Sin42)= F 42˚ We can use Sin as the question involves the Opposite length and the Hypotenuse 7cm F The rule we use is: Opposite Hypotenuse Sinϴ= F 7 Sin42= 7 (Sin42)= F 4.68 cm (2dp)= F

Sin Example 2 H 10cm Opposite Sinϴ= 10 Hypotenuse Sin17= H 17˚ We can use Sin as the question involves the Opposite length and the Hypotenuse H 10cm The rule we use is: Opposite Hypotenuse Sinϴ= 10 H Sin17= H x Sin17= 10 H= 10 Sin17 H= 34.2 cm (1dp)

Cosine (cos) Adjacent Cosϴ= Hypotenuse Adjacent Hypotenuse 50˚ We use cosine when we have the Adjacent length and the Hypotenuse Hypotenuse The rule we use is: Adjacent Hypotenuse Cosϴ= Adjacent

Cos Example 1 9cm Adjacent Cosϴ= Hypotenuse A A Cos53= 9 9 x Cos53= A 53˚ We can use Cos as the question involves the Adjacent length and the Hypotenuse 9cm The rule we use is: Adjacent Hypotenuse Cosϴ= A A 9 Cos53= 9 x Cos53= A 5.42 cm (2dp)= A

Cos Example 2 H 9cm Adjacent Cosϴ= 9 Hypotenuse Cos17= H H x Cos17= 10 17˚ We can use Cos as the question involves the Adjacent length and the Hypotenuse H 9cm The rule we use is: Adjacent Hypotenuse Cosϴ= 9 H Cos17= H x Cos17= 10 H= 9 Cos17 H= 9.41 cm (2dp)

Tangent (tan) Opposite Tanϴ= Adjacent 10cm 6.4cm (1dp) 50˚ We use tangent when we have the Opposite and Adjacent lengths. 10cm The rule we use is: Opposite Adjacent Tanϴ= 6.4cm (1dp)

Tan Example 1 11cm Opposite Tanϴ= O Adjacent O Tan53= 11 11 x Tan53= O 53˚ We can use Tan as the question involves the Adjacent and Opposite lengths 11cm The rule we use is: Opposite Adjacent Tanϴ= O O 11 Tan53= 11 x Tan53= O 14.6 cm (1dp)= O

Tan Example 2 A 21cm Opposite Tanϴ= Adjacent 21 Tan35= A A x Tan35= 21 35˚ We can use Tan as the question involves the Adjacent and Opposite lengths A The rule we use is: 21cm Opposite Adjacent Tanϴ= 21 A Tan35= A x Tan35= 21 A= 21 Tan35 A= 29.99 cm (2dp)

There are a few ways to remember this The three rules So we have: Opposite Hypotenuse Adjacent Hypotenuse Opposite Adjacent Sinϴ= Cosϴ= Tanϴ= O H A H O A Sinϴ= Cosϴ= Tanϴ= SOHCAHTOA There are a few ways to remember this

Practice 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: H 15cm 60˚ Sinϴ= Opposite Hypotenuse O 50˚ 17cm H 22cm 60˚ Cosϴ= Adjacent Hypotenuse 25cm 38˚ A Tanϴ= Opposite Adjacent 60˚ O A 42˚ 15cm 11cm

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

Finding missing angles Trigonometry Day 5 Finding missing angles

Some Old Hairy Camels Are Hairier Than Other Animals SOHCAHTOA Opposite Hypotenuse Adjacent Hypotenuse Opposite Adjacent Sinϴ= Cosϴ= Tanϴ=

Find the missing angle SOH CAH TOA 7cm 3cm ϴ This question will use Sin O H 7cm Sinϴ= 3cm Sinϴ= 3 7 Hypotenuse opposite Sinϴ=0.42857... ϴ What angle would give us this answer? You could use the ANS button on your calculator Sin-1ANS= ϴ Sin-10.42857...= ϴ 25.4˚ (1dp)= ϴ

Find the missing angle SOH CAH TOA 6cm ϴ 8cm This question will use Tan O A Tanϴ= 6cm ϴ Tanϴ= 8 6 Adjacent Tanϴ=1.25 What angle would give us this answer? 8cm Opposite Tan-11.25= ϴ 51.3˚ (1dp)= ϴ

Find the missing angle SOH CAH TOA 12cm 9cm ϴ This question will use Cos A H 12cm Cosϴ= 9cm ϴ Cosϴ= 9 12 Hypotenuse Adjacent Cosϴ=0.75 What angle would give us this answer? You could use the ANS button on your calculator Cos-1ANS= ϴ Cos-10.75= ϴ 41.4˚ (1dp)= ϴ

Practice Questions Answers: ϴ 23cm 35cm 11cm ϴ 10cm 17cm ϴ ϴ 18cm 12cm 50.2˚ 28.6˚ 59.1˚ 52.3˚ 63.4˚ 65.4˚ 40.9˚ Practice Questions ϴ 23cm 35cm 11cm ϴ 10cm 17cm ϴ ϴ 18cm 12cm 22cm ϴ 12cm 20cm 11cm 13cm ϴ ϴ ϴ 10cm 5cm 6cm 15cm

Let’s 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 Answers: 8cm 22.2cm 48.6 ˚ 41.8 ˚ 58.1 ˚ 16cm 42.7 ˚ 19.5cm 11cm 19.3˚ 41 ˚ 21.6cm 60 ˚ 11.7cm 55.5 ˚ 49.8 ˚ Find the missing lengths and angles 1 2 3 ϴ 4 16cm X 12cm X 15cm 8cm 30˚ 51˚ ϴ 14cm 17cm 5 6 7 8 ϴ ϴ 36cm 18cm 19cm X X 9cm 11.2cm 63˚ 35˚ 8.3cm 9 10 11 12 15cm 50˚ ϴ 46cm 53cm X 40cm X 43˚ 28˚ X 23cm 16 13 14 15 ϴ 32cm ϴ 106cm 16cm X 61cm 74cm 18˚ 36cm 81cm ϴ

Use sin, cos and tan to find the missing lengths, round them to 1 d 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. Side Length (rounded to 1 dp) a b c d e f g h i a b c d e f g h i 10cm 30˚ 40˚ 50˚ 35˚ 45˚ 42˚ 27˚ 38˚ 51˚

Use sin, cos and tan to find the missing lengths, round them to 1 d 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. Side Length (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 Side Length (rounded to 1 dp) a b c d e f g h i a b c d e f g h i 10cm 30˚ 40˚ 50˚ 35˚ 45˚ 42˚ 27˚ 38˚ 51˚

Extra-Practice Answers: 3.1cm 6.1cm 5.1cm 17.1cm 4.5cm 8.6cm 20.5cm