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
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