VIDYA BHARTI EDUCATIONAL INSTITUTIONS

HOW TO REMEMBER THE TRIGONOMETRIC TABLE

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Did you ever have any trouble

remembering the sine or tangent of

an angle?This explains how you can easily find

the basic trigonometric

numbers of the most common

angles.

STEPS

CREATE A TABLEIn the first row, write down the trigonometric ratios (sin, cos, tan, cot). In the first column, write down the angles (0°, 30°, 45°, 60°, 90°). Leave other entries

FILL IN THE SIN COLUMN We will fill in the blank entries in the sin column using the expression √x/2. Once the sine column is filled, we'll be able to fill all other columns effortlessly!

For the 1st entry in the sine column (that is, sin 0°), set x = 0 and plug it in the expression √x/2. Thus, sin 0° = √0/2 = 0/2 = 0

For the 2nd entry in the sine column (that is, sin 30set x = 1 and plug it in the expression √x/2. Thus, sin 30° = √1/2 = 1/2

For the 3rd entry in the sine column (that is, sin 45°), set x = 2 and plug it in the expression √x/2. Thus, sin 45° = √2/2 = 1/√2

For the 4th entry in the sine column (that is, sin 60°),set x = 3 and plug it in the expression √x/2. Thus, sin 60° = √3/2.

For the 5th entry in the sin column (that is, sin 90°), set x = 4 and plug it in the expression √x/2. Thus, sin 90° = √4/2 = 2/2 = 1.

FILL IN THE COSINE COLUMNSimply copy the entries in the sine column in reverse order into the cosine column. This is valid because sin x° = cos (90-x)° for any x.

FILL IN THE TANGENT COLUMNWe know that tan = sin / cos. So, for every angle take its sin value and divide it by the cos value to get the corresponding tan value. For example, tan 30° = sin 30° / cos 30° = (√1/2) / (√3/2) = 1/√3

FILL IN THE COTANGENT COLUMNSimply copy the entries in tangent column in reverse order into the cot column. This is valid because tan x° = sin x° / cos x° = cos (90-x)° / sin (90-x)° = cot (90-x)° for any x.

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