Trigonometric Values Table – Complete Guide with Formulas, Charts & Practice Questions

📌 What is the Trigonometric Values Table?

The Trigonometric Values Table is a quick reference for the values of six trigonometric functions—sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot)—at standard angles: 0°, 30°, 45°, 60°, and 90°. These values are vital for solving height & distance problems, simplifications, and trigonometric identities.

📊 Trigonometric Values Table (0° to 90°):

Here’s the standard trigonometric values chart you must memorize:

✅ Tip to Remember:
The sin values follow the pattern of √0/2, √1/2, √2/2, √3/2, √4/2 from 0° to 90°.

📐Mnemonic to Remember the Table Easily:

Here’s a fun way to recall sine values:

sin(0°) = √0/2  
sin(30°) = √1/2  
sin(45°) = √2/2  
sin(60°) = √3/2  
sin(90°) = √4/2 

Now reverse it for cos values:

cos(0°) = √4/2   
cos(30°) = √3/2  
cos(45°) = √2/2  
cos(60°) = √1/2  
cos(90°) = √0/2 

This is the quickest hack to recall the trigonometric values table without rote learning!

🧮 Formulas Involving Trigonometric Ratios:

Here are essential trigonometric formulas based on the trigonometric values table:

✳️ Reciprocal Identities:

• sin θ = 1 / cosec θ
• cos θ = 1 / sec θ
• tan θ = 1 / cot θ

✳️ Quotient Identities:

• tan θ = sin θ / cos θ
• cot θ = cos θ / sin θ

✳️ Pythagorean Identities:

• sin² θ + cos² θ = 1
• 1 + tan² θ = sec² θ
• 1 + cot² θ = cosec² θ

📈 Graphical Representation of Trigonometric Values:

A visual reference helps in better memory retention:

|  sin θ  | Increasing from 0 to 1 ➡  
|  cos θ  | Decreasing from 1 to 0 ➡  
|  tan θ  | Increases sharply, undefined at 90°  

✅ How to Use the Trigonometric Values Table:

Let’s go through an example:

Example 1:
Find the value of
sin 30° + cos 60° + tan 45°

Using the table:
sin 30° = 1/2
cos 60° = 1/2
tan 45° = 1

Total = 1/2 + 1/2 + 1 = 2

🧠 Common Exam Questions Based on Trigonometric Values:

Q1) Evaluate: (sin 30° + cos 60°) ÷ tan 45°
Ans: (1/2 + 1/2) ÷ 1 = 1

Q2) What is the value of:

sec 60° + cosec 30°
Ans: sec 60° = 2, cosec 30° = 2 → Total = 4

Q3) Find the value of:

sin² 45° + cos² 45°
Ans: (1/√2)² + (1/√2)² = 1/2 + 1/2 = 1

📚 Practice Questions (For You to Try):

Try solving these using the trigonometric values table:

1. Find the value of sin 60° + cos 30°
2. Evaluate tan 60° × cot 30°
3. What is the value of sin 45° ÷ cos 45°?
4. Calculate sec 30° + cosec 60°
5. Find (tan 30° + tan 60°) ÷ tan 45°

📩 Answers

Solution 1:
sin 60° = √3/2
cos 30° = √3/2
sin 60° + cos 30° = √3/2 + √3/2 = (2√3)/2 = √3
✅ Answer: √3

Solution 2:
tan 60° = √3
cot 30° = √3
tan 60° × cot 30° = √3 × √3 = 3
✅ Answer: 3

Solution 3:
sin 45° = 1/√2
cos 45° = 1/√2
sin 45° ÷ cos 45° = (1/√2) ÷ (1/√2) = 1
✅ Answer: 1

Solution 4:
sec 30° = 2/√3
cosec 60° = 2/√3
sec 30° + cosec 60° = 2/√3 + 2/√3 = 4/√3
✅ Answer: 4/√3

Solution 5:
tan 30° = 1/√3
tan 60° = √3
tan 45° = 1
(tan 30° + tan 60°) ÷ tan 45° = (1/√3 + √3) ÷ 1 = 4/√3
✅ Answer: 4/√3

📘 Real-Life Application of Trigonometric Values Table:

• In engineering, to calculate slopes, angles, and distances
• In architecture, to determine building dimensions
• In astronomy, for finding the positions of celestial objects
• In government exams, to solve quantitative aptitude questions quickly

💡 Tips to Memorize the Table Faster:

• Write it down daily for 7 days
• Use flashcards or sticky notes
• Practice 5 quick sums every day
• Pair angles (like sin 30° = cos 60°) to remember better
• Use digital apps or games like quizlet

🔁 Extended Trigonometric Values (120°, 135°, 150°, 180°):

As exams sometimes test trigonometric values beyond 90°, here’s an extended mini table:

📌 Note: Values are based on ASTC rule (All, Sin, Tan, Cos in different quadrants).

📝 Conclusion:

Mastering the trigonometric values table is not about memorizing blindly, but understanding the logic and patterns. Once you do that, you’ll solve complex questions in just seconds. This guide is your perfect companion for SSC, RRB, NDA, and other competitive exams.

🧠 Keep practicing. Keep revising. The trigonometric values table will become your best friend in math success!

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