Trigonometry 1 Introduction Labelling sides with respect to

Trigonometry 1 Introduction Labelling sides with respect to angles Sin, cos or tan to find lengths?

What is Trigonometry? : Warm up Solve for x 1) 20= X 2 2) 15= X 3 3) 8= 32 X 4) 7= 5) 16= 21 X 64 X Go to Corbett Maths video Trigonometry Introduction 329 • 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

COPY IN YOUR BOOKS Labelling the sides in a right angled triangle Hypotenuse The hypotenuse is always the longest side. It never touches the right angle It is opposite the right angle Hypotenuse Opposite The Opposite is the side opposite the angle you are working with. Adjacent The Adjacent is the side next to the angle you are working with. It touches that angle. Hypotenuse Opposite

Labelling the sides Adjacent Opposite 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. . But if we are working with this angle, we label the sides like this. . . ϴ Opposite Adjacent

Now try labelling the sides in these Right Angle Triangles 10 multiple choice questions

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

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

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

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

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

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

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

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

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

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

COPY IN YOUR BOOKS • 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 have looked at the three rules and have practised labelling triangles. • We will now have to decide whether we are using Sin, Cos or Tan when answering questions.

Copy this in your books. a° Adjacent Hypotenuse Opposite Sin a° = Opposite Cos a° = Hypotenuse Tan a° = Opposite Adjacent Hypotenuse

Some Old Hairy Camels Are Hairier Than Other Animals Opposite Sine a° = Hypotenuse Adjacent Cos a° = Hypotenuse Tan a° = Opposite Adjacent

When to use Sin SOH We can use Sin as the question involves the x Opposite length 7 cm 42˚ The rule we use is: and the Hypotenuse Sine = Opposite Hypotenuse

When to use Cos CAH We can use Cos as the question involves the Adjacent length 7 cm 56˚ x The rule we use is: and the Hypotenuse Cos = Adjacent Hypotenuse

When to use Tan TOA We can use Tan as the question involves the Opposite length 8 cm The rule we use is: 65˚ x and the Adjacent Tan = Opposite Adjacent

SOH CAH TOA This question will use Sine opposite X Hyp 7 cm ote nus e 35˚ O Sinϴ= H X Sin 35= 7

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

SOH 43˚ CAH TOA This question will use Sin O Sinϴ= H 8 Hyp X Sin 43= ote X nus e 8 cm opposite

Adjacent SOH X 26˚ CAH TOA This question will use Cosine O cosϴ= A Hyp ote X nus cos 26= e 8 8 c m

Sin, Cos or Tan? 10 multiple choice questions

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

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

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

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

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

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

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

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

Will you use Sin, Cos or Tan with this question? 63˚ 3. 4 cm X A) Cos C) Sin B) Tan

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