Trigonometry Table: Ratios, Values & Examples

Table of Contents  

• What is a Trigonometry Table
• Trigonometry Ratios Table
• How to Remember the Trigonometry Table
• Trigonometry Table Formulas
• Trigonometry Chart Explanation
• Solved Examples on Trigonometry Table
• Conclusion

What is a Trigonometry Table

A trigonometry table is a chart that shows the values of sine, cosine, tangent, and other ratios for common angles - 0°, 30°, 45°, 60°, and 90°. These values are important for solving various trigonometric problems without a calculator. The table includes values for sine, cosine, tangent, cotangent, secant, and cosecant. It simplifies calculations and aids in solving trigonometric equations. 
 

Trigonometry Ratios Table

Learning ratios of trigonometric table is helpful in many ways. It is applied in the field of engineering and navigation. It has been in use since the pre-digital era, even before the pocket calculators came into existence. It has also contributed to the development of the very first mechanical computing devices.

Here’s the standard trigonometry table for quick reference: 

 

How to Remember Trigonometry Table

Use these tips to help remember the trigonometry table:  

• Finger Rule: Use your fingers to recall sin and cos values for 0°, 30°, 45°, 60°, and 90°.  

• Patterns: Look for patterns in sin and cos values, as they reflect each other.  

• Mnemonics: Use phrases like "Some People Have Curly Brown Hair Till Painted Black" to remember sin, cos, tan, etc.  

• Practice: Solve multiple questions using the trigonometry chart until it feels natural.  
  
  

Trigonometry Table Formulas: 

Before learning trigonometry table remember these basic trigonometry formulas as they will help you to check trigonometry rules and solve problems with angles and sides.

• sin²θ + cos²θ = 1  

• 1 + tan²θ = sec²θ  

• 1 + cot²θ = cosec²θ  

• sin θ = Opposite / Hypotenuse  

• cos θ = Adjacent / Hypotenuse  

• tan θ = Opposite / Adjacent  

• cot θ = 1/tan θ  

• sec θ = 1/cos θ  

• cosec θ = 1/sin θ  

Trigonometry Chart Explanation

A trigonometry chart visually represents the trigonometric ratios for various angles. It helps in:  

• Understanding how trigonometric functions behave.  

• Identifying values that increase or decrease with the angle.  

• Supporting easier recall of trigonometric table values.  
  
  

Solved Examples on Trigonometry Table

Example 1:  

Find the value of sin 30° and cos 60°.  

Solution:  

According to the trigonometry table,  

sin 30° = 1/2, cos 60° = 1/2.  

 
Example 2:  

Verify that sin²45° + cos²45° = 1.  

Solution:  

sin 45° = 1/√2, cos 45° = 1/√2.  

So, (1/√2)² + (1/√2)² = 1/2 + 1/2 = 1.  

Example 3:  

Find tan 60° using the trigonometry chart.  

Solution:  

tan 60° = √3.  

Example 4:  

Find cot 30° and cosec 30°.  

Solution:  

cot 30° = √3, cosec 30° = 2 (from the trigonometry table).  

Example 5:  

Use the identity to find sec θ if tan θ = √3.  

Solution:  

We apply the identity:  

1 + tan²θ = sec²θ.  

1 + 3 = sec²θ → sec²θ = 4 → sec θ = 2.  

 
Conclusion

Trigonometry is more than just a collection of formulas; it's a powerful mathematical tool used in science, engineering, and everyday life. By learning what trigonometry is, remembering the table, and using simple formulas, you can solve even tough problems with ease. Regular practice with the trigonometry chart and solving real-life examples will help achieve mastery in this topic. Start your journey into the world of trigonometry today to discover how essential and exciting this subject can be! 

Master the Trigonometry Table with expert guidance at Orchids The International School.