Trigonometry can seem daunting at first glance, but understanding it opens up a world of mathematical and practical possibilities. Whether you’re a student preparing for exams or a professional needing to brush up on your skills, mastering the trigonometric table is a crucial step. This guide will walk you through effective tips and tricks to learn the trigonometric table with ease and confidence.

What is the Trigonometric Table?

The trigonometric table is a chart that provides the values of trigonometric functions—sine, cosine, and tangent—for specific angles. These functions are fundamental in mathematics, helping us to understand and solve problems involving right-angled triangles and circles.

Key Trigonometric Functions

Sine (sin): The sine of an angle is the ratio of the length of the opposite side to the hypotenuse in a right-angled triangle.

Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the hypotenuse.

Tangent (tan): The tangent of an angle is the ratio of the length of the opposite side to the adjacent side.

Tips and Tricks to Learn Trigonometric Table

Find tricks to remember formula, signs and table of trigonometry ratios:

Some People Have Curly Brown Hair Turned Permanently Black

Sine (sin):

• S from Some stands for Sine
• P from People stands for Perpendicular
• H from Have stands for Hypotenuse

Cosine (cos):

• C from Curly stands for Cosine
• B from Brown stands for Base
• H from Hair stands for Hypotenuse

Tangent (tan):

• T from Turned stands for Tangent
• P from Permanently stands for Perpendicular
• B from Black stands for Base

Add Sugar To Coffee (ASTC)

In trigonometry, the ASTC technique helps you remember whether a trigonometric function is positive or negative in each of the four quadrants:

First Quadrant

• Add : All (Sine, Cosine, and Tangent) are all positive.

Second Quadrant

• Sugar: Sine is positive.
• Cosine and Tangent are negative.

Third Quadrant

• To: Tangent is positive.
• Sine and Cosine are negative.

Fourth Quadrant

• Coffee: Cosine is positive.
• Sine and Tangent are negative.

Steps to Create a Trigonometric Ratios Table

Steps to make Trigonometric table are given below:

Step 1: Make a table listing the top row of angles as 0°, 30°, 45°, 60°, 90° and write all trigonometric functions in the first column as sin, cos, tan, cot, sec, cosec.

Step 2: Find Sine Values

• Write down the angles (0°, 30°, 45°, 60°, 90°) in ascending order.
• Allocate them values (0, 1, 2, 3, 4) according to the order.
• Divide the values by 4 and take the square root of the entire value.

Angle	0°	30°	45°	60°	90°
Step A	0	1	2	3	4
Step B	0/4	1/4	2/4	3/4	4/4
Step C	√(0/4)	√(1/4)	√(2/4)	√(3/4)	√(4/4)
Sin	0	1/2	1/√2	√3/2	1

Step 3: Find Cosine Values

Once you’ve determined the sine values, the cosine values can be easily calculated using the fact that [Tex]\cos(\theta) = \sin(90° – \theta)[/Tex]. You just have to write the above line from right to left.

Step 4: Find Tangent Values

Tangent values are calculated by dividing sine values by cosine values.

Step 5: Find Cotangent, Secant, and Cosecant Values

These can be found by taking the reciprocals of the values you’ve already calculated.

Step 6: Fill in the Table

Complete the table with the calculated values.

By following these steps, you’ll have a complete trigonometric ratios table for the specified angles.

Important Trigonometry Formulas

Below are some of the periodic identities:

• sin(90°−θ) = cos θ
• cos(90°−θ) = sin θ
• tan(90°−θ) = cot θ
• cot(90°−θ) = tan θ
• sec(90°−θ) = cosec θ
• cosec(90°−θ) = sec θ

Below is the list of trigonometric ratios, including sine, cosine, secant, cosecant, tangent and cotangent with their formulas:

Functions	Abbreviation	Relationship to sides of a right triangle
Sine Function	sin	Opposite side/ Hypotenuse
Tangent Function	tan	Opposite side / Adjacent side
Cosine Function	cos	Adjacent side / Hypotenuse
Cosecant Function	cosec	Hypotenuse / Opposite side
Secant Function	sec	Hypotenuse / Adjacent side
Cotangent Function	cot	Adjacent side / Opposite side

Reciprocal Trigonometry Formulas

Reciprocal Identities are as follows:

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

Solved Questions on Trigonometric Table and Formulas

Question 1: Show that tan 10° tan 15° tan 75° tan 80° =1 using trigonometry formulas

Solution:

We have, 

L.H.S = tan 10° tan 15° tan 75° tan 80°

= tan(90-80)° tan 15° tan(90-15)° tan 80°

= cot 80° tan 15° cot 15° tan 80°

=(cot 80° × tan 80°)( cot 15° × tan 15°)

= 1 = R.H.S

Example 2: A person is standing at a distance of 10 meters from the base of a building. The person measures the angle of elevation to the top of the building as 60°. What is the height of the building?

Solution:

Given: Base = 10 m

Angle of elevation = 60°

Let h be the height of the building.

As tan θ = Perpendicular/Base

⇒ tan(60°) = h / 10

⇒ h = 10 tan(60°)

Using the values of tan(60°) = √3, we get:

 h = 10√3 ≈ 17.32 m

Therefore, the height of the building is approximately 17.32 meters.

Related Articles:

• Trigonometry in Maths: Table, Formulas, Identities and Ratios
• Trigonometry Formulas – List of All Trigonometric Identities and Formulas
• Trigonometric Values

FAQs on Solved Questions on Trigonometric Table and Formulas

What are trigonometric tables, and how are they used?

Trigonometric tables provide values of trigonometric functions (like sine, cosine) for different angles. They’re used to quickly find these values, essential for solving trigonometric problems involving angles and sides of triangles.

How do I use trigonometric formulas in problem-solving?

Trigonometric formulas like sine, cosine, and tangent relate angles and sides of triangles. By applying these formulas, you can solve for unknown angles or side lengths in a triangle.

What strategies are useful for solving trigonometric problems?

Strategies include identifying triangle types, using trigonometric ratios, Pythagorean theorem, trigonometric identities, and special triangle properties.

How do I choose the right trigonometric function for a problem?

The choice depends on given information and what you’re solving for. If you know two sides, use sine, cosine, or tangent depending on what’s given and what you’re finding.

What are real-world applications of trigonometry?

Trigonometry is used in engineering, physics, architecture, navigation, etc., for calculating distances, heights, analyzing forces, designing structures, and navigating using GPS or celestial observations.