Homeclass 10MathsIntroduction to TrigonometryTrigonometric Table

Trigonometric Table

The trigonometric table is a reference chart that provides the exact values of trigonometric ratios for standard angles, specifically 0, 30, 45, 60, and 90 degrees. It is an essential mathematical tool used to solve right-angled triangles and evaluate expressions without requiring complex calculations.

Key Concepts

The table covers all six trigonometric ratios: sine, cosine, tangent, cosecant, secant, and cotangent for the primary standard angles.

The values of cosine for standard angles are simply the values of sine written in reverse order, because sine and cosine are complementary ratios.

Tangent values are calculated by dividing the sine value by the cosine value for each respective angle.

Certain ratios at specific angles, such as tangent of 90 degrees or cosecant of 0 degrees, are not defined because their calculation involves division by zero.

Formula & Equation

sin(A) values for 0, 30, 45, 60, and 90 degrees are derived using the square roots of 0/4, 1/4, 2/4, 3/4, and 4/4 respectively. This yields 0, 1/2, 1/root(2), root(3)/2, and 1.

A represents the standard angle (0, 30, 45, 60, or 90 degrees).

Common Misconceptions

Myth: Students often think that the value of tan 90 degrees is 0.

Fact: The value of tan 90 degrees is actually undefined. This is because tangent is calculated as sine divided by cosine, and cos 90 degrees is 0. Division by zero is not defined in mathematics.

Real World Applications

Carpenters use standard trigonometric values to cut wood at precise 30-degree or 45-degree angles for roof trusses and staircases.

Surveyors use the known values of 60-degree angles to quickly calculate the height of a building or a tree using a simple clinometer and basic multiplication.

Frequently Asked Questions

What is the easiest way to remember the trigonometric table?

You only need to memorize the sine values (0, 1/2, 1/root(2), root(3)/2, 1). Cosine is the reverse of sine, and tangent is found by dividing sine by cosine.

Why are standard angles like 30, 45, and 60 degrees used in the trigonometric table?

These specific angles frequently appear in geometry, particularly in equilateral and isosceles right triangles, making their exact ratio values easy to derive and highly useful for everyday calculations.

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