Trigonometry Formulas for Class 10 PDF Download – Complete Guide with Examples

📘 What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of a right-angled triangle. The word ‘trigonometry’ is derived from the Greek words trigonon (triangle) and metron (measure).

In Class 10, the focus is primarily on:

• Understanding trigonometric ratios
• Using identities and formulas
• Solving triangles
• Applying these in real-life and word problems

🔢 Trigonometric Ratios Table (Basic):-

The six basic trigonometric ratios are:

🧠 Memory Tip: SOH-CAH-TOA:-

To remember the trigonometric ratios easily, use:

SOH – Sin = Opposite / Hypotenuse
CAH – Cos = Adjacent / Hypotenuse
TOA – Tan = Opposite / Adjacent

📊 Trigonometric Ratios of Standard Angles:-

🧮 Important Trigonometry Formulas for Class 10:-

Here are the most used trigonometry formulas for Class 10:

✅ Reciprocal Identities:-

1. cosec θ = 1 / sin θ
2. sec θ = 1 / cos θ
3. cot θ = 1 / tan θ

✅ Quotient Identities:-

4. tan θ = sin θ / cos θ
5. cot θ = cos θ / sin θ

✅ Pythagorean Identities:-

6. sin²θ + cos²θ = 1
7. 1 + tan²θ = sec²θ
8. 1 + cot²θ = cosec²θ

📐 Pythagorean Theorem – Definition & Formula:-

The Pythagorean Theorem is a fundamental relation between the sides of a right-angled triangle. It is the foundation of many trigonometric concepts taught in Class 10.

🔷 Statement:

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

🔢 Formula:

Hypotenuse² = Base² + Height²

Or in simple terms:

c² = a² + b²

Where:

• c = hypotenuse (longest side, opposite the right angle)
• a and b = the two other sides (base and height)

🖼️ Diagram of Pythagorean Theorem:-

Here is a visual diagram of a right-angled triangle applying the Pythagorean Theorem:

✏️ Example 1

Q: In a right triangle, the base is 6 cm and the height is 8 cm. Find the hypotenuse.

Solution:
Base = 6 cm
Height = 8 cm

Using the formula:
Hypotenuse² = 6² + 8² = 36 + 64 = 100
Hypotenuse = √100 = 10 cm

✏️ Example 2

Q: A ladder is placed against a wall. It reaches 12 meters high on the wall and is 5 meters away from the wall at the base. Find the length of the ladder.

Solution:
This forms a right-angled triangle:
Height = 12 m, Base = 5 m

Length of ladder = Hypotenuse
Hypotenuse² = 12² + 5² = 144 + 25 = 169
Hypotenuse = √169 = 13 m

🧠 Pythagorean Theorem in Trigonometry:-

The Pythagorean identity in trigonometry is derived from this theorem:

sin²θ + cos²θ = 1

It shows the same relationship between the perpendicular and base relative to the hypotenuse in a unit circle or right triangle.

📝 Practice Questions (With Answers):-

1. The sides of a triangle are 5 cm and 12 cm. Find the hypotenuse.
   • Answer: √(5² + 12²) = √169 = 13 cm
2. A tree is broken and the top touches the ground 15 meters away. If the broken part is 20 meters long, find the height from which the tree broke.
   • Answer: √(20² – 15²) = √175 = ≈13.2 m
3. If the hypotenuse of a right triangle is 17 cm and one side is 8 cm, find the other side.
   • Answer: √(17² – 8²) = √(289 – 64) = √225 = 15 cm

📘 Applications of Trigonometry in Real Life:-

Even though it looks theoretical, trigonometry has real-life uses in:

• Measuring heights and distances
• Construction and architecture
• Navigation and GPS
• Astronomy

In Class 10, questions often revolve around finding the height of a tree or a building using trigonometric ratios based on angles of elevation or depression.

🧠 Examples of Trigonometry Problems:-

Example 1: If sin θ = 3/5, find cos θ and tan θ.

Solution:
Given, sin θ = Opposite / Hypotenuse = 3/5
Using Pythagoras:
Adjacent = √(5² – 3²) = √(25 – 9) = √16 = 4

So,
cos θ = 4/5
tan θ = 3/4

Example 2: If tan A = 1, find the value of sin²A + cos²A.

Solution:
We know:
sin²A + cos²A = 1 (Always true for any angle)
So, the answer is 1

Example 3: Find the value of: sin 30° * cos 60° + cos 30° * sin 60°

Solution:
= (1/2)(1/2) + (√3/2)(√3/2)
= 1/4 + 3/4 = 1

✍️ Practice Questions:-

Try these questions on your own to test your understanding:

1. If cos θ = 5/13, find sin θ and tan θ.
2. Prove: sin²A + cos²A = 1
3. Find the value of: tan 45° + cot 45°
4. If tan A = √3, find sin A and cos A.
5. A ladder 10 m long is leaning against a wall making an angle of 60° with the ground. Find the height it reaches on the wall.

📥 Trigonometry Formulas for Class 10 PDF Download:-

To make your revision easier, we have compiled all important trigonometry formulas for Class 10 in a PDF format. This handy document is great for last-minute revisions and offline study.

Click below to get your Trigonometry Formulas for Class 10 PDF Download: 🔽 [Download PDF]

This PDF includes:

• All essential formulas
• Standard angles chart
• Identities
• Reciprocal, quotient and Pythagorean formulas

Make sure to print and stick it on your study wall!

🎯 Tips to Master Trigonometry in Class 10:-

• Understand the triangle and label sides correctly.
• Memorize trigonometric ratios and formulas regularly.
• Practice questions involving angles of elevation and depression.
• Revise standard angles table often.
• Download and keep the trigonometry formulas for Class 10 PDF download handy.

🧾 Conclusion:-

Trigonometry may seem tough at first, but with consistent practice and clear understanding of the formulas, it becomes a scoring topic. Focus on understanding the logic behind each ratio, apply them in problems, and revise using the trigonometry formulas for Class 10 PDF download we’ve provided above.

Happy Learning! 📚

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