Trigonometry Formulas Class 10

Last Updated : 16 Nov, 2023

Trigonometry Formula in Class 10 is the list of all formulas used in Trigonometry useful for class 10 students in their exams. Trigonometry is the branch of mathematics that establishes the relation of the angle of a right triangle with the ratio of sides. Trigono means triangle and metron means measure. There are in total six trigonometric ratios namely, sine, cosine, tangent, cotangent, secant, and cosecant. The Trigonometric Formulas establish relations between these Trigonometric Ratios.

In this article, we will learn Trigonometric Formulas essential for Class 10 along with the Trigonometric Ratio Table.

What is Trigonometry Ratio?

Trigonometric Ratios are the ratio of sides of a right triangle for a given value of the angle denoted as theta(Î¸). There are six trigonometric ratios namely, sine, cosine, tangent, cotangent, secant, and cosecant. The angle Î¸ is defined as the angle between the base and the hypotenuse of the right triangle.

Trigonometric Ratio Formulas Class 10

Trigonometric Ratio Formulas establish the relation between Trigonometric Ratios and the sides of a right triangle. The T-Ratios Formulas Class 10 are listed below:

• sin Î¸ = Perpendicular/Hypotenuse
• cos Î¸ = Base/Hypotenuse
• tan Î¸ = Perpendicular/Base
• cosec Î¸ = Hypotenuse/Perpendicular
• sec Î¸ = Hypotenuse/Base
• cot Î¸ = Base/Perpendicular

Trigonometric Ratio Table Class 10

Trigonometric Ratio Table contains the value of all the six trigonometric ratios at some standard angles 0Â°, 30Â°, 45Â°, 60Â° and 90Â°.

Î¸

0Â°

30Â°

45Â°

60Â°

90Â°

sin Î¸

0

1/2

1/âˆš2

âˆš3/2

1

cos Î¸

1

âˆš3/2

1/âˆš2

1/2

0

tan Î¸

0

1/âˆš3

1

âˆš3

Not defined

cosec Î¸

Not defined

2

âˆš2

2/âˆš3

1

sec Î¸

1

2/âˆš3

âˆš2

2

Not defined

cot Î¸

Not defined

âˆš3

1

1/âˆš3

0

All Trigonometry Formulas Class 10

List of all Trigonometric Formulas essential for Class 10 is mentioned below:

Trigonometric Reciprocal Identities

• sin Î¸ = 1/cosec Î¸ â‡’ cosec Î¸ = 1/sin Î¸
• cos Î¸ = 1/sec Î¸ â‡’ sec Î¸ = 1/cos Î¸
• tan Î¸ = 1/cot Î¸ â‡’ cot Î¸ = 1/tan Î¸

Trigonometric Identities

• sin2Î¸ + cos2Î¸ = 1
• 1 + tan2Î¸ = sec2Î¸
• 1 + cot2Î¸ = cosec2Î¸

Complementary Angle Formulas

• sin(90 – Î¸) = cos Î¸
• cos(90 – Î¸) = sin Î¸
• tan(90 – Î¸) = cot Î¸
• cot(90 – Î¸) = tan Î¸
• sec(90 – Î¸) = cosec Î¸
• cosec(90 – Î¸) = sec Î¸

Supplementary Angle Formulas

• sin(180 – Î¸) = sin Î¸
• cos(180 – Î¸) = -cos Î¸
• tan(180 – Î¸) = -tan Î¸
• cot(180 – Î¸) = -cot Î¸
• sec(180 – Î¸) = -secÎ¸
• cosec(180 – Î¸) = cosec Î¸

Even and Odd Angle Formulas

• sin(-Î¸) = -sin Î¸
• cos(-Î¸) = cos Î¸
• tan(-Î¸) = -tan Î¸
• cot(-Î¸) = -cot Î¸
• sec(-Î¸) = sec Î¸
• cosec(-Î¸) = -cosec Î¸

Double Angle Formulas

• sin 2Î¸ = 2sinÎ¸.cosÎ¸
• cos 2Î¸ = 1 – 2sin2Î¸
• tan 2Î¸ = 2tanÎ¸/(1-tan2Î¸)

Also, Check

Solved Examples on Trigonometry Formulas Class 10

Example 1: If sin A = 3/4. Calculate cos A and tan A

Solution:

cos2A = 1 – sin2A

â‡’ cos2A = 1-(9/16)

â‡’ cos2A = 7/16

â‡’ cosA = âˆš7/4

â‡’ tanA = sinA/cosA

â‡’ tanA = 3/âˆš7

Example 2: Given 15 cot A = 8. Find sin A and sec A

Solution:

cotA = 8/15

â‡’ cosec2A = 1 + cot2A

â‡’ cosec2A = 1 + (64/225)

â‡’ cosec2A = 289/225

â‡’ cosecA = 17/15

â‡’ sinA = 15/17

â‡’ secA = cosecA/cotA

â‡’ secA = 17/8

Example 3: Find the value of sin 45Â° – cos 45Â°.

Solution:

sin 45Â° = cos 45Â° = 1/âˆš(2)

â‡’ sin 45Â° – cos 45Â° = 0

Example 4: If tan Î¸ + cot Î¸ = 7. Find tan2Î¸ + cot2Î¸

Solution:

tan Î¸ + cot Î¸ = 7

â‡’ (tanÎ¸ + cotÎ¸)2 = 49

â‡’ tan2Î¸ + cot2Î¸ + 2tanÎ¸cotÎ¸ = 49

â‡’ tan2Î¸ + cot2Î¸ + 2 = 49

â‡’ tan2Î¸ + cot2Î¸ = 47

Example 5: The value of tan Î¸ = 3/4. Find the value of sec Î¸.

Solution:

1 + tan2Î¸ = sec2Î¸

â‡’ 1 +(3/4)2 = sec2Î¸

â‡’ sec2Î¸ = 25/16

â‡’ secÎ¸ = 5/4

Example 6: If sec Î¸ + tan Î¸ = 5. Find sec Î¸ – tan Î¸.

Solution:

sec 2Î¸ – tan 2Î¸ = 1

â‡’ (sec Î¸ + tan Î¸)(sec Î¸ – tan Î¸) = 1

â‡’ 5(sec Î¸ – tan Î¸) = 1

â‡’ sec Î¸ – tan Î¸ = 1/5

Practice Questions on Trigonometric Formulas Class 10

1. Prove that (cos Î¸/(1 – tan Î¸)) + (sin Î¸/(1 – cot Î¸)) = sin Î¸ + cos Î¸.

2. Prove that tan2Î¸ + cot2Î¸ +2 = sec2Î¸ * cosec2Î¸.

3. If cosec Î¸ + cot Î¸ = 9. find cos Î¸.

4. If cos Î¸ = 4/5. Find all other trigonometric ratios.

5. Find the value of sin 60Â° cos 30Â° + cos 30Â° sin 60Â°.

6. Find the value of tan 30Â°/cot 60Â°.

7. Find the value of (sin 30Â° + cos 30Â°) – (sin 60Â° + cos 60Â°).

8. If tanÎ¸ + cotÎ¸ = 1. Find the value of tan10Î¸ + cot10Î¸.

9. Find the value of sin 45Â° + cos 45Â°.

10. Find the value of cos 19Â°/sin 71Â°.

Trigonometry Formula Class 10 – FAQs

1. What are Trigonometric Ratio Formulas in Class 10.

Trigonometric Ratio Formulas establish the relation between Trigonometric Ratios and the sides of a right triangle.

cotÎ¸ = 1/tanÎ¸

3. What is the value of sin(-Î¸)?

sin(-Î¸) = -sinÎ¸

4. What is the relation between cot Î¸ and cosec Î¸?

1 + cot2Î¸ = cosec2Î¸

5. How is tan Î¸ related to sin Î¸ and cos Î¸?

tan Î¸ = sin Î¸/cos Î¸

sin 30 = 1/2

7. How is cosecÎ¸ related to sinÎ¸?

cosecÎ¸ = 1/sinÎ¸

tan 45 = 1

cos(-Î¸) = cosÎ¸

10. Is Trigonoimetry Formula Class 10 important?

Yes, Trigonometry Formula Class 10 is very important for Class 10 students as they can always expect questions from this in their exams.

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