How to Memorise the Trigonometry Table Fast: Tips & Tricks
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: All Trigonometric Ratios, Values & PDF
1. What is a trigonometry table and why is it important in Maths?
A trigonometry table lists the values of the six trigonometric ratios (sin, cos, tan, cosec, sec, cot) for standard angles like 0°, 30°, 45°, 60°, and 90°. It is important because it provides a quick reference to solve problems in geometry, calculus, and various scientific fields without needing to recalculate the values from scratch each time. It forms the foundation for understanding the relationships between angles and side lengths in a right-angled triangle.
2. What are the six fundamental trigonometric ratios shown in the table?
The six fundamental trigonometric ratios, derived from the sides of a right-angled triangle (Perpendicular, Base, Hypotenuse), are:
- Sine (sin) = Perpendicular / Hypotenuse
- Cosine (cos) = Base / Hypotenuse
- Tangent (tan) = Perpendicular / Base
- Cosecant (cosec) = Hypotenuse / Perpendicular (reciprocal of sin)
- Secant (sec) = Hypotenuse / Base (reciprocal of cos)
- Cotangent (cot) = Base / Perpendicular (reciprocal of tan)
3. Is there a trick to remember the values for sin, cos, and tan in the trigonometry table?
Yes, there is a simple method to create the table for standard angles (0°, 30°, 45°, 60°, 90°):
- For Sine (sin): Write the numbers 0, 1, 2, 3, 4. Divide each by 4, and then take the square root. For example, sin 60° = √(3/4) = √3/2.
- For Cosine (cos): Simply write the sine values in reverse order. So, cos 0° is the same as sin 90°, which is 1.
- For Tangent (tan): Divide the corresponding sine value by the cosine value (tan θ = sin θ / cos θ). For instance, tan 30° = sin 30° / cos 30° = (1/2) / (√3/2) = 1/√3.
4. What are some real-world applications of the concepts shown in the trigonometry table?
The principles of trigonometry and its values are crucial in many real-world fields. For example:
- Astronomy: To calculate the distance between celestial bodies.
- Navigation: Used in GPS and satellite systems to pinpoint locations.
- Engineering: For designing structures like bridges and buildings and calculating forces.
- Geography: In cartography for creating accurate maps.
- Physics: To describe and analyse sound and light waves.
5. How are the trigonometric ratios in the table related to each other?
The trigonometric ratios are interconnected through fundamental identities. The primary relationships are:
- Reciprocal Identities: cosec θ = 1/sin θ, sec θ = 1/cos θ, and cot θ = 1/tan θ.
- Quotient Identities: tan θ = sin θ / cos θ and cot θ = cos θ / sin θ.
For example, to find the value of tan 45° using this relationship, you can divide sin 45° (1/√2) by cos 45° (1/√2), which equals 1. This shows how knowing one value can help you derive another.
6. Why do some values in the trigonometry table, like tan 90°, appear as 'Not Defined'?
A value in the trigonometry table is 'Not Defined' when its calculation involves division by zero, which is mathematically impossible. For example:
- tan 90° is calculated as sin 90° / cos 90°. Since sin 90° = 1 and cos 90° = 0, this becomes 1/0, which is not defined.
- Similarly, cosec 0° is calculated as 1 / sin 0°. Since sin 0° = 0, this results in 1/0, which is also not defined.
7. How are the values from the trigonometry table extended for angles greater than 90°, such as 180° or 270°?
For angles beyond 90°, the concept of quadrants in the Cartesian coordinate system is used. The signs (positive or negative) of the trigonometric ratios change depending on the quadrant the angle falls into, following the ASTC rule (All, Sine, Tangent, Cosine). The numerical value is determined by its corresponding acute angle in the first quadrant. For example, cos 120° is in the second quadrant, where only sine is positive. Therefore, cos 120° = -cos(180°-60°) = -cos 60° = -1/2.
