Introduction to Trigonometric Ratios CXC

Introduction to Trigonometric Ratios CXC

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What is Trigonometry ?

Trigonometry is a branch of mathematics that studies triangles and the relationship between their sides and the angles between these sides.

The word ‘TRIGONOMETRY’ is derived from the Greek words ‘TRI’ (meaning three ), ‘GON’ ( meaning sides ) and‘ METRON’ ( meaning measure.

Pythagoras Theorem

• In any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of areas of the squares whose sides are the two legs.

• In the figure AC² = AB² + BC² 

find the value of C

find the value of C

Sometimes it is not always practical to find the length of sides of a right triangle using Pythagoras theorem

Therefore we need to learn some new mathematics to carry out our calculations

At the end of this session students will be able to 

•  State the three basic trigonometric ratios (sine, cosine, tangent) 

•  Use scientific calculator to find the sine, cosine and tangent of any angle less than or equal to 90°

Investigation

How to remember the trigonometric ratios - SOHCAHTOA

• sin=opposite/hypotenuse

• cos=adjacent / hypotenuse

• tan=opposite/ adjacent

Labelling the sides in a right triangle

• Side opposite 90° will always be hypotenuse.

• Side opposite to given acute angle will always be perpendicular or opposite

• Remaining side will be base or adjacent

Using sin, cos or tan to find the side or angle of a right triangle.

• Identify the sides or angles

• Choose the right trig ratio based on what was given.

• Solve the equation to find the unknown