Trigonometry Table- Formula, Trick, Selected Questions & Answers

Ever wondered how to swiftly solve trigonometry problems without breaking a sweat? Dive into the world of trigonometry tables, your ultimate ally in mastering angles and triangles.

In this article, we will explore how these tables simplify complex mathematical equations and boost your problem-solving skills.

Role Of Trigonometric Table & Ratio 

Trigonometry tables typically include sine, cosine, and tangent, along with their reciprocal functions, such as cosecant, secant, and cotangent.

Trigonometric ratios play a crucial role in mathematics. It deals with the relationships between angles and sides of triangles.

Trigonometry Table With Ratios

Provided below is a trigonometry table containing all the ratios from 0° to 360° degrees in angle and radian value:

Trigonometric Functions Table 

Provided below is the table of trigonometric functions table:

Trick To Memorize Trigonometric Ratios

Let us study how you, as a student, can memorize trigonometric ratios easily:

Using Mnemonic

Utilize mnemonics like SOH-CAH-TOA to remember trig ratios:

sine = opposite/hypotenuse

cosine = adjacent/hypotenuse

tangent = opposite/adjacent

Trick To Memorize Trigonometric Table

Memorizing trigonometric tables is important, and it is quite simple. Provided below is a simple yet useful trick to memorize trigonometry tables and ratios like never before using the one-hand trick:

Calculating Trigonometric Values

Let us study how to calculate respective trigonometric values:

Value Of Sinθ

To determine the sinθ values, divide 0, 1, 2, 3, and 4 by 4 under the root, respectively. Let's take, for example, the value sin0° of √0/4= 0

Value Of Cosθ

The cos value, cosθ, is calculated differently from the sine value, sinθ. To find cosθ, divide 4 by the number you used to find sinθ. For instance, if you divided 4 by 4 to get sin0°, then you would also divide 4 by 4 to determine cos0°.

Value Of Tanθ

The tangent of an angle (tanθ) is calculated by dividing the sine of the angle (sinθ) by the cosine of the angle (cos). For example, to find the tangent value at 0 degrees, simply divide the sine value at 0 degrees by the cosine value at 0 degrees: tan 0°= 0/1= 0.

Value Of Cotθ

The value of cotθ is equal to the reciprocal of tan. The value of cot at 0° will be obtained by dividing 1 by the value of tan at 0° as cot 0°= 1/0= Infinite or not defined.

Value Of Cosecθ

The value of cosecθ at 0° is the reciprocal of sin at 0° as cosec 0°= 1/= Infinite or not defined.

Value Of Secθ

All reciprocal values of cosθ can determine the value of secθ. The value of secθ on 0° is the opposite of cosθ on 0°.

Click here to learn more about various topics related to quantitative aptitude, including trigonometry tables and ratios.

Selected Practice Questions With Answers

Practice your trigonometry skills by attempting challenging problems that require using the trigonometry table. Provided below as some selected questions of trigonometry with detailed answers:

Question 1: If tan θ + cot θ = 2, then what is the value of tan ^(100) θ + cot^(100) θ?

a) 1

b) 2

c) 3

d) 4

Answer: b) 2

Question 2: If a sin 45 = b cosec 30, what is the value of a^4/b^4?

a) 2^3

b) 4^3

c) 6^3

d) none of the above

Answer: b) 4^3

Question 3: Which of the following is the correct value of cot 10.cot 20.cot 60.cot 70.cot 80?

a) 1/√3

b) √3

c) -1

d) 1

Answer: a) 1/√3

Question 4: What is the value of tan(45°)?

a) 1/(2)^1/2

b) 1/2

c) 1

d) 0

Answer: c) 1

Question 5: What is the value of sin(90°)?

a) 1

b) 0

c) 1/2

d) 3/2

Answer: a) 1

Question 6: Which of the following trigonometric functions represents the ratio of the length of the side adjacent to an acute angle in a right triangle to the length of the hypotenuse?

a) Sine

b) Cosine

c) Tangent

d) Secant

Answer: b) Cosine

Question 7: If sin(θ) = 0.6 and cos(θ) = 0.8, what is the value of tan(θ)?

a) 0.48

b) 0.64

c) 0.75

d) 1.33

Answer: c) 0.75

Explanation: sin(θ) = 0.6

cos(θ) = 0.8

We know that tan(θ) = sin(θ) / cos(θ)

Substituting the given values:

tan(θ) = 0.6 / 0.8 = 0.75

Question 8: If sin(α)=3/5​ and cos(α)=4/5, what is the value of tan(α)?

a) 3/4

b) 4/3

c) 3/5

d) 4/5

Answer: a) 3/4

Explanation: sin⁡(α)=3/5

cos⁡(α)=4/5

tan⁡(α)=sin⁡(α)/cos⁡(α)

Substituting the given values, tan⁡(α)=3/5÷4/5

tan⁡(α)=3/5×5/4

tan⁡(α)=3/4.

Question 9: In a right triangle, if the length of the side opposite the right angle (hypotenuse) is 10 units and the length of the side adjacent to the angle is 6 units, what is the value of the sine of the angle?

a) 0.6

b) 0.8

c) 0.75

d) 0.625

Answer: a) 0.6

Explanation: Length of the hypotenuse (opposite the right angle) = 10 units

Length of the adjacent side = 6 units

We need to find the sine of the angle.

We know that:

sin⁡(θ)=opposite side/hypotenuse

Substituting the given values,

sin⁡(θ)=6/10=0.6

Question 10: If sin⁡(θ)=3/5, what is the value of cos⁡(θ)?

a) 4/5

b) 3/4

c) 5/3

d) 5/4

Answer: a) 4/5

Conclusion

You've now mastered essential trigonometry functions, memorization tricks, and creating tables. Calculating sine and cosine values, understanding tangent and cotangent, and determining cosecant and secant values are no longer a challenge.

Practical applications have become clearer, and you're ready to enhance your skills with practice questions. Keep practising to solidify your knowledge and ace any trigonometry-related tasks that come your way.

Frequently Asked Questions (FAQs)

1. What are the essential trigonometry functions?

Essential trigonometry functions include sine, cosine, tangent, cotangent, cosecant, and secant. Each function is explained with examples to help you understand their significance in trigonometry.

2. How can I easily memorize trigonometry concepts?

Utilize mnemonic devices, practice regularly, and break down complex concepts into smaller parts for better retention.

3. What is the importance of creating trigonometry tables?

Creating trigonometry tables helps in quick reference and calculation of sine and cosine values. The step-by-step guide in the blog post will assist you in constructing these tables efficiently for your studies or work.

4. How do I calculate sine and cosine values using trigonometry tables?

This article offers a detailed explanation of calculating sine and cosine values using trigonometry tables. Understand the process step-by-step to accurately determine these values for various angles.

5. What practical applications can I explore with trigonometry tables?

Discover practical applications of trigonometry tables in fields like engineering, physics, astronomy, and more. By mastering these tables through practice questions provided in the blog post, you can enhance your problem-solving skills effectively.

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