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Trigonometry

Maths: Edexcel IGCSE Higher, topic 4.6.2

Trigonometry

Sin, cos and tan relate an angle and two sides in a right-angled triangle.

Formula triangles

Formula triangles

  • Formula triangles can be used to remember the ratios (SOHCAHTOA) and to rearrange the ratios so they can be used.
  • The side opposite the angle being used is referred to as the ‘opposite’ and the side next to the angle being used is called the ‘adjacent’.
Sin

Sin

Cos

Cos

Tan

Tan

Angle of elevation

Angle of elevation

  • The angle of elevation of an object above an observer relative to the observer is the angle between the horizontal and the line from the object to the observer's eye.
  • The angle of depression of an object below an observer relative to the observer is the angle between the horizontal and the line from the object to the observer's eye.

Trigonometry in 3D

Trigonometry can be used to solve problems in three dimensions.

Example

Example

  • What is the size of the angle between the line AH and the plane ABCD?
Identify the right-angled triangle

Identify the right-angled triangle

  • We must find the lower angle of the triangle AHC to answer the question.
  • We can use the equation:
  • tanθ=HCAC=2.5ACtan\theta = \frac{HC}{AC} = \frac{2.5}{AC}
Work out the length of AC

Work out the length of AC

  • We can use pythagoras' theorem to work out the length of AC.
  • 32+42=5\sqrt{3^2 + 4^2} = 5
  • AC = 5 cm.
Work out the angle

Work out the angle

  • Substituting the side lengths into our previous equation we have:
  • θ=tan−1(2.55)=26.57\theta = tan^{-1}(\frac{2.5}{5}) = 26.57°

Test yourself on Trigonometry

  • For opposite ÷ adjacent, which trig function should we use?

  • For opposite ÷ hypotenuse, which trig function should we use?

  • What is sin(0)?

  • What is sin(90)?

  • What is cos(0)?

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