ICSE Class 9 Answered

Table of trigonometric ratios of standar angles is given below

Standard angles are 0° , 30° , 45° , 50° and 90° .

If we remeber sine ratios of standard angles , we get remaing other ratios .

Only we have to memorise the sine ratio.

Make it easy to remeber sin 0° = 0 and sin 90° = 1

To remember trigonometric ratio of standard angles , we can use the right triangle having angles 30° and 60°.

Also we can use the isoceless right triangle for 45°

Sides ratio of the right angle triangle  having angles 30° and 60°  is   1 : √3 : 2 .

If side opposite to angle 30° is 1 , then side opposite to angle 60° is  √3 and hypotneuse is 2

Hence by using ΔABC , we get

sin30° = AC/BC = 1/2

cos30° = AB/BC = √3/2

tan30° = AC/AB = 1/√3

sin60° = AB/BC = √3/2

cos60° = AC/BC = 1/2

tan60° = AB/AC = √3

Sides ratio of the isoceless right angle triangle having other angles as 45°  is   1 : 1 : √2

If equal sides are of unit length , then length of hypotenuse .is √2 .

We can check the following ratios from ΔPQR

sin45° = cos45° =  1 / √2

tan45° =  1

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If two angles are α and β and their sum α + β = 90° , then the angles α and β are complementry angles .

For complementry angles α and β , we have the following property

sin α = cos β

cos α = sin β

Angles 30° and 60° are complimentry angles .Hence we have

sin 30° = cos 60° = 1/2

cos 30° = sin 60° = √3 / 2

Similarly for complimentry angles 45° and 45°

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tan θ = ( sin θ ) / ( cos θ )

hence if we know sine ratio and cosine ratio of an angle , then tangent can be calculated