Exact Trigonometry Table Values of Sin Cos Tan Cosec Sec and Cot
The concept of trigonometry table plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Mastering the trigonometry table helps students quickly recall sine, cosine, tangent, and other trigonometric function values for standard angles, making problem-solving much faster and more accurate.
What Is Trigonometry Table?
A trigonometry table is a chart that lists the exact and decimal values of the six primary trigonometric ratios—sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot)—for important angles such as 0°, 30°, 45°, 60°, and 90°. You’ll find this concept applied in areas such as triangle calculations, navigation, engineering, and physics.
Standard Trigonometry Table (0°, 30°, 45°, 60°, 90°)
Memorising the trigonometry table allows students to solve geometric and real-world problems efficiently. Here is the most important trigonometry table you should know:
| Function / Angle | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin θ | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | Not Defined |
| cosec θ | Not Defined | 2 | √2 | 2/√3 | 1 |
| sec θ | 1 | 2/√3 | √2 | 2 | Not Defined |
| cot θ | Not Defined | √3 | 1 | 1/√3 | 0 |
Key Formula for Trigonometry Table
The core trigonometric ratios are defined as follows for right-angled triangles:
- sin θ = Perpendicular / Hypotenuse
- cos θ = Base / Hypotenuse
- tan θ = Perpendicular / Base
- cosec θ = 1/sin θ = Hypotenuse / Perpendicular
- sec θ = 1/cos θ = Hypotenuse / Base
- cot θ = 1/tan θ = Base / Perpendicular
How to Memorise the Trigonometry Table?
Here are smart tricks to help you remember the trig ratios for the standard angles:
-
Count 0, 1, 2, 3, 4 for sin θ. Divide each by 4 and take the square root:
sin 0° = √0/2 = 0sin 30° = √1/2 = 1/2sin 45° = √2/2 = 1/√2sin 60° = √3/2 = √3/2sin 90° = √4/2 = 1 - For cos θ, reverse the order of sin θ values!
- tan θ = sin θ / cos θ for the same angle.
- Cosec, sec, and cot are just reciprocals of sin, cos, and tan respectively.
- Tip: The hand trick—number your fingers 0–4. Sine is √n/2 (counting from the thumb for angles 0° to 90°).
Trigonometry Table Values (0° to 360°)
For class 10, 11, JEE and other exams, you may need trigonometry table values from 0° up to 360°. Use the sign convention:
- All trigonometric ratios are positive in the 1st quadrant (0°–90°).
- Only sin and cosec are positive in the 2nd quadrant (90°–180°).
- Only tan and cot are positive in the 3rd quadrant (180°–270°).
- Only cos and sec are positive in the 4th quadrant (270°–360°).
Knowing these sign rules helps you find sine, cosine, and tangent for any angle up to 360° using reference angle tricks.
Step-by-Step Illustration: Using the Table
Example 1. Calculate sin 45° + cos 30°
1. From trigonometry table: sin 45° = 1/√2, cos 30° = √3/22. Add: \( \frac{1}{\sqrt{2}} + \frac{\sqrt{3}}{2} \)
3. Rationalise if required or use decimal approximations.
Example 2. Find tan 60°
1. From the table: tan 60° = √3.2. Final answer: tan 60° = √3 ≈ 1.732.
Speed Trick or Vedic Shortcut
To recall the trigonometry values fast for MCQ exams, remember: for sin, go up (0 to 90°), for cos, go down (90° to 0°). Use the table as a shortcut when solving height and distance questions.
Memory Power Tip: For sin values, the formula is sin θ = √n/2, where n = 0 for 0°, up to n = 4 for 90°.
Try These Yourself
- What is the value of cos 60°?
- Verify if tan 45° × cot 45° equals 1.
- Find sin 30° + cos 60°.
- What is sec 90°?
- Use the table to check if cot 0° is defined.
Frequent Errors and Misunderstandings
- Mixing up sine and cosine orders
- Forgetting that tan 90° and sec 90° are undefined
- Confusing degree and radian input for calculators
Relation to Other Concepts
The trigonometry table connects closely with trigonometric ratios and trigonometric identities. These values are used across geometry, heights and distances, and even calculus.
Classroom Tip
A quick way to remember trigonometric table values is to visualise the SOHCAHTOA mnemonic or use the table hand-trick. Vedantu’s maths teachers often share such shortcuts for exam success in class 10 and foundation trigonometry classes.
We explored the trigonometry table—from its definition, formula derivation, memory shortcuts, example questions, and how it links to other maths ideas. Practise using this table and explore more free learning resources at Vedantu to boost your maths confidence!
Explore related topics: Trigonometric Ratios, Trigonometric Ratios of Complementary Angles, Trigonometric Identities, Trigonometric Functions Domain & Range
FAQs on Trigonometry Table for Standard Angle Values
1. What is a trigonometry table?
A trigonometry table is a chart that lists the standard values of trigonometric ratios like sin, cos, tan, cosec, sec, and cot for commonly used angles. It usually includes angles such as 0°, 30°, 45°, 60°, and 90°. These values are used to quickly solve trigonometric problems without a calculator and are fundamental in geometry, algebra, and calculus.
2. What are the standard trigonometric values in the trigonometry table?
The standard trigonometric values are the exact values of sin θ, cos θ, and tan θ for special angles like 0°, 30°, 45°, 60°, and 90°.
- sin 30° = 1/2, cos 30° = √3/2
- sin 45° = 1/√2, cos 45° = 1/√2
- sin 60° = √3/2, cos 60° = 1/2
- tan 45° = 1
- sin 0° = 0, cos 0° = 1
3. How do you remember the trigonometry table easily?
You can remember the trigonometry table using the square root pattern method for sin θ and cos θ.
- Write numbers: 0, 1, 2, 3, 4
- For sin θ: √(number)/2
- For cos θ: reverse order √(4−number)/2
4. What is the value of tan 0°, 30°, 45°, 60°, and 90°?
The values of tan θ for standard angles are derived using tan θ = sin θ / cos θ.
- tan 0° = 0
- tan 30° = 1/√3
- tan 45° = 1
- tan 60° = √3
- tan 90° is not defined
5. Why is tan 90° undefined in the trigonometry table?
The value of tan 90° is undefined because it involves division by zero. Since tan θ = sin θ / cos θ and cos 90° = 0, the expression becomes 1/0, which is mathematically undefined. Therefore, tan 90° does not have a real value in the trigonometry table.
6. What is the difference between sin and cos in the trigonometry table?
The main difference is that sin θ represents the ratio of opposite side to hypotenuse, while cos θ represents adjacent side to hypotenuse in a right triangle. In the trigonometry table:
- Sin values increase from 0 to 1 between 0° and 90°
- Cos values decrease from 1 to 0 between 0° and 90°
7. How is the trigonometry table derived?
The trigonometry table is derived using special right-angled triangles like the 30°–60°–90° and 45°–45°–90° triangles.
- In a 45°–45°–90° triangle, sides are 1, 1, √2
- In a 30°–60°–90° triangle, sides are 1, √3, 2
8. What are reciprocal trigonometric ratios in the trigonometry table?
The reciprocal trigonometric ratios are cosec θ, sec θ, and cot θ, which are the reciprocals of sin θ, cos θ, and tan θ respectively.
- cosec θ = 1/sin θ
- sec θ = 1/cos θ
- cot θ = 1/tan θ
9. How do you use the trigonometry table to solve problems?
You use the trigonometry table by substituting known angle values into trigonometric expressions. For example, to find sin 60° + cos 60°:
- sin 60° = √3/2
- cos 60° = 1/2
- Sum = (√3 + 1)/2
10. What are the common mistakes students make while learning the trigonometry table?
Common mistakes include confusing values of sin and cos, and forgetting that tan 90° is undefined.
- Mixing up sin 30° (1/2) and cos 30° (√3/2)
- Forgetting tan 90° is undefined
- Not remembering reciprocal ratios correctly
- Using degrees instead of radians incorrectly in advanced problems
