Usually, a calculator is used to find the trigonometric ratios at different values. But sometimes, the problem may ask to solve it without using a calculator where it involves some standard angles. The standard angles are 0, 300, 450, 600 and 900. Let us learn how to find the values of trigonometric ratios of these standard angles without using a calculator.
Trigonometric ratios of 300 and 600:
Consider an equilateral triangle ABC whose side is 2 units.
Then AB=BC=CA=2.
Let AD be the altitude.
Then BD=1.
From Pythagoras theorem, we get AD = √3.
From ΔABD, (using definitions of trigonometric ratios)
Sin 60 = √3/2 => Cosec 60 = 2/ √3
Cos 60 = 1/2 => Sec 60 = 2
Tan 60 = √3 => Cot 60 = 1/√3
Again from ΔABD, (using definitions of trigonometric ratios)
Sin 30 = 1/2 => Cosec 30 = 2
Cos 30 = √3/2 => Sec 30 = 2/√3
Tan 30 = 1/√3 => Cot 30 = √3.
Trigonometric ratios of 450:
Consider an isosceles right angled triangle ABC with right angle at B where AB=BC =1 unit.
Using definitions of trigonometric ratios,
Sin 45 = 1/√2 => Cosec 45 = √2
Cos 45 = 1/√2 => Sec 45 = √2
Tan 45 = 1 => Cot 45 = 1.
Based on the above data, the following table is formed.
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