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A trigonometry table is a reference chart for trigonometry, a branch of math studying angles and triangles. It lists the values of sine (sin), cosine (cos), tangent (tan), and other trigonometric functions for different angles, from 0° to 360°.
Before calculators, these tables were important for solving problems in navigation, science, and engineering. They were so important that they even led to the creation of the first mechanical calculators!
Trigonometry tables are especially useful for right triangles (triangles with a 90° angle). By looking up the angle and the relevant function (sin, cos, etc.), you can find the ratio of the triangle’s sides. This makes solving many geometrical problems much easier.
While calculators have made them less common, trigonometry tables are still a valuable tool for understanding these functions and their applications.Let us read this article to clear your doubts regarding trigonometry table.
Table of Contents
What is a Trigonometry Table?
Tables of trigonometric functions are helpful in many different areas of mathematics. Prior to the invention of pocket calculators, trigonometric tables were important for scientific research, engineering, and navigation.Let’s have a look at the specific angle value-based trigonometry formulas:
| θ | 0° | 30° | 45° | 60° | 90° | 180° |
| Sin | 0 | 1/2 | 1/2 | 3/2 | 1 | 0 |
| Cos | 1 | 3/2 | 1/2 | 1/2 | 0 | -1 |
| Tan | 0 | 1/3 | 1 | 3 | ∞ | 0 |
| Cot | ∞ | 3 | 1 | 1/3 | 0 | ∞ |
| Sec | 1 | 2/3 | 2 | 2 | ∞ | -1 |
| Cosec | ∞ | 2 | 2 | 2/3 | 1 | ∞ |
How to Remember a Trigonometry Table?
Don’t worry about memorizing the trigonometry table! With a few important formulas, you can learn the table in no time.
These formulas relate the trigonometric values (sine, cosine, tangent) of one angle to another. The magic number? 90 degrees!
Here’s the trick to solve such questions based on trigonometry table :
- To find the sine, cosine, or tangent of any angle, subtract it from 90 degrees and look up that value in your table. The corresponding sine becomes your cosine, cosine becomes sine, and tangent becomes cotangent (and vice versa).
- By memorising these relationships and just a few table values, you can derive the rest! This technique is much easier than rote memorization and opens the door to solving many trigonometry problems.
Must Read:21 Trignometry Formulas for Competitive Exams
How to Create a Trigonometry Table?
These steps provide a systematic approach to filling out a trigonometry table with values for various angles and trigonometric functions.
Step 1: Setting up the Table
- Create a table with angles listed in the top row, such as 0°, 30°, 45°, 60°, 90°, etc.
- In the first column, list all trigonometric functions: sin, cos, tan, cosec, sec, cot.
Step 2: Determining sin Values
- For each angle, divide 0, 1, 2, 3, 4 by 4 under the root, respectively.
- For example, sin 0° = 0, sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, sin 90° = 1.
Step 3: Determining cos Values
- Cos-values are opposite to sin-values. Divide by 4 in the opposite sequence of sin.
- For example, cos 0° = 1, cos 30° = √3/2, cos 45° = 1/√2, cos 60° = 1/2, cos 90° = 0.
Step 4: Determining tan Values
- Tan is sin divided by cos (tan = sin/cos).
- For example, tan 0° = 0/1 = 0, tan 30° = (1/2) / (√3/2) = 1/√3, tan 45° = 1/(1/√2) = √2, and so on.
Step 5: Determining cot Values
- Cot is the reciprocal of tan.
- For example, cot 0° = 1/0 = ∞, cot 30° = 1/(1/√3) = √3, cot 45° = 1/1 = 1, and so on.
Step 6: Determining cosec Values
- Cosec is the reciprocal of sin.
- For example, cosec 0° = 1/0 = ∞, cosec 30° = 1/(1/2) = 2, cosec 45° = 1/(1/√2) = √2, and so on.
Step 7: Determining sec Values
- Sec is the reciprocal of cos.
- For example, sec 0° = 1/1 = 1, sec 30° = 1/(√3/2) = 2/√3, sec 45° = 1/(1/√2) = √2, and so on.
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FAQs
Seven basic trigonometric formulas: Sine, Cosine, Tangent, Cosecant, Secant, Cotangent, and their reciprocal relationships.
Trigonometry has numerous formulas, including trigonometric identities, angle addition, double angle, half angle, and Pythagorean identities.
Six fundamental trigonometric formulas: Sine, Cosine, Tangent, Cosecant, Secant, Cotangent, representing ratios of sides in right triangles.
A trigonometry value table lists angles alongside their corresponding trigonometric function values: sine, cosine, tangent, cosecant, secant, and cotangent.
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