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Hwa Chong Institution
Integrated Programme/SBGE
Secondary Two Mathematics
Name: ______________________ ( )

Class: _________

Date: _______________

Trigonometry

Lesson Package

Unit 7 – Trigonometry

1
...
The first work on
trigonometric functions was produced by the Greek mathematician Hipparchus in
about 140 BC on the topic of chords in a circle
...
This makes Hipparchus the founder of trigonometry
...

1
...
These functions relate the
angles in the triangle to the ratio of the length of the sides with respect to each other
...

Thus,
5 cm
sin 30
=
hypotenuse

5 cm
sin 30
5 cm

0
...
3 Trigonometric ratios of special angles

sin 0  0
1
sin 30 =
2
1
sin 45 =
2
3
sin 60 =
2
sin 90 = 1
2

cos 0  1
3
2
1
cos 45 =
2
1
cos 60 =
2
cos 90 = 0
cos 30 =

tan 0  0
1
tan 30 =
3
tan 45 = 1
tan 60 = 3
tan 90 = undefined

1
...
5 Addition and difference formulae
cos(   )
α

sin(   )

sin  sin 

1

sin  cos 
β
α

cos  cos 

Therefore,
sin(   )  sin  cos   sin  cos 
cos(   )  cos  cos   sin  sin 

cos  cos 
α

sin 

sin  sin 

sin  cos 

1
β
α-β

cos(   )

Therefore,
sin(   )  sin  cos   sin  cos 
cos(   )  cos  cos   sin  sin 

4

sin(   )

Then what about tan(   ) and tan(   )? In order to solve this question you have to
learn…
… trigonometric identities!
1
...

5

1
...
It is the reciprocal function of tan
...
8 Trigonometric identities (3)
By Pythagoras Theorem,
opposite 2  adjacent 2  hypotenuse 2
opposite 2
adjacent 2
hypotenuse 2


hypotenuse 2 hypotenuse 2 hypotenuse 2
opposite 2
adjacent 2
(
) (
) 1
hypotenuse
hypotenuse

sin 2   cos 2   1
Knowing this, we can derive other trigonometric identities
...
9 Real life applications of trigonometry
Trigonometry can be used to find the height of structures or mountains by utilizing few
measurements
...


Height
80 m
Height=(tan60 )(80 m)
tan 60 

 80 3 m
Indians in 6th century were able to work out the distance ratio between moon-earth and
sun-earth by realizing that when they see a half moon, the angle between earth-moon-sun
has to be a right angle and they can use their trigonometric functions to work out what the
distance to the sun is, relative to the distance to the moon

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