Volume 22, Number 4, April 2013
Extension
Mathskit: using trigonometry
Ian Harding
This issue’s Mathskit includes the following statements:
cos 60° = sin 30°
sin 60° = cos 30°
cos 60° = sin 30° = 0.5
sin 60° = cos 30° = √3/2 ≈ 0.866
and we suggested that you have a go at deriving the values listed.
<Please insert diagram supplied in separate pdf file>
The diagram shows a right-angled triangle ABC with angles 30° and 60° and a hypotenuse, c, which is
2 units long. You can see that it is half of an equilateral triangle, so its shortest side, a, must be 1 unit
long.
a=1
c=2
Using Pythagoras’s Theorem,
2
2
2
2
2
2
a +b =c
b =c –a
=4–1
=3
b = √3 = 1.732
From the definitions of the trigonometric ratios in the magazine, we can write:
cos 60° = sin 30° = a/c = ½ = 0.5
sin 60° = cos 30° = b/c = √3/2 = 0.866...
tan 60° = b/a = √3 = 1.732...
tan 30° = a/b = 1/√3 = 0.577...
Philip Allan Publishers © 2013
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