Remember the Trigonometric Table
Did you ever have any trouble remembering the sine or tangent of an angle? This article explains how you can easily find the basic trigonometric numbers of the most common angles.
Contents
Steps
- Create a table.
In 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 blank. - Fill in the sine 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 30°), set 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.
- For the 1st entry in the sine column (that is, sin 0°), set x = 0 and plug it in the expression √x/2.
- Fill in the cosine column.
Simply 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 column.
We 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 column.
Simply 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.
Tips
- Do not leave irrational numbers in the denominator. For example, tan30° = 1/√3. Don't leave it that way. Instead, write it like √3/3.
Warnings
- You can't divide by 0! tan90° = ±∞ and cot0° = ±∞, but ∞ isn't considered an actual number, so don't write it. Write "not defined" or "n/a" (not applicable) instead.
