S2B

Chapter 11

Introduction to Trigonometric Ratios

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The term ‘trigonometry’ originated from two Greek words with meaning ‘surveying’ and ‘triangle’. Therefore this knowledge is related to triangle surveying.

Trigonometry was first developed by astronomers from Greece, Persia and Arabia in around 200AD.

Origin of Trigonometry

2009 Chung Tai Educational Press. All rights reserved.©

Origin of Trigonometry

Regiomontanus (1436 - 1476), a German mathematician, arranged the knowledge of trigonometry systematically and made it a branch of mathematics.

2009 Chung Tai Educational Press. All rights reserved.©

D

E

Similar Right-angled TrianglesWhen an acute angle is fixed (say 35) in a right-angled triangle ABC, the ratios of any two sides in ABC are the same as the corresponding ratios in a triangle similar to ABC.

A

B

C

i.e.BC DEAB ADAC AEAB ADBC DEAC AE

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Cosine Ratio of an AngleIn any right-angled triangle ABC, the ratio of the adjacent side to the hypotenuse of B is known as ‘the cosine ratio of B’, denoted by ‘cos B’.

cos B Adjacent sideHypotenuse

i.e.

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Sine Ratio of an AngleIn any right-angled triangle ABC, the ratio of the opposite side to the hypotenuse of B is known as ‘the sine ratio of B’, denoted by ‘sin B’.

sin B Opposite sideHypotenuse

i.e.

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Tangent Ratio of an AngleIn any right-angled triangle ABC, the ratio of the opposite side to the adjacent side of B is known as ‘the tangent ratio of B’, denoted by ‘tan B’.

tan B Opposite sideAdjacent side

i.e.

The End