JEE Main 2025: Trigonometry Notes - FREE PDF Download

The  Trigonometry chapter covers the relationships between the angles and sides of triangles, focusing on trigonometric functions such as sine, cosine, tangent, and their inverses. This is a crucial chapter for JEE Main Exams, and you can expect at least 2 to 3 questions from it. Check out how many questions were asked from the Trigonometry chapter in the last five years of JEE Main exams.

Take the chance to elevate your preparation with our Trigonometry Notes. It covers the JEE Main Maths syllabus, which you can download for FREE.

Top Concepts to Study in Trigonometry for JEE Main 2025

Here, you will review the main topics in Trigonometry. These crucial topics can truly improve your preparation. Good at them will give you a big advantage in the upcoming test. So, let's discuss the essential topics you need to consider for success in JEE Main 2025.

• Basic Trigonometric Functions

• Trigonometric Ratios and Identities

• Trigonometric Equations

• Trigonometric Inverse Functions

• Trigonometric Equations and Identities

• Sum and Product of Trigonometric Functions

• Trigonometric Limits

• Trigonometric Equations and Graphs

• Properties of Trigonometric Functions

• Applications of Trigonometry

• Trigonometric Formulas

• Polar Coordinates and Complex Numbers

How Trigonometry can Shape your JEE Main 2025 Journey?

Trigonometry, a seemingly intricate realm of mathematics, plays a pivotal role in shaping your JEE Main 2025 journey, offering mathematical skills and a toolkit to unravel complex problems across diverse domains. Its significance reverberates beyond exams, grounding you in fundamental principles that transcend disciplines and support your academic and professional growth.

Here are a few features that make the Chapter important for JEE Main exam 2025:

Foundational Mathematical Language:

Trigonometry forms an essential language for understanding angles, triangles, and circular relationships, building a bridge between geometry and algebra.

Problem-solving Powerhouse:

The ability to manipulate trigonometric functions empowers you to solve intricate problems in physics, engineering, and various scientific fields.

Trigonometric Functions Mastery:

Grasping sine, cosine, tangent, and their derivatives equips you to model periodic phenomena, from oscillations to waveforms.

Geometric and Algebraic Fusion:

Trigonometry combines geometric insights with algebraic techniques, expanding your mathematical versatility.

Real-world Applications:

Trigonometry's applications span physics (waves, vibrations), engineering (circuits, structures), and beyond, making it indispensable in practical scenarios.

Vectors and Trigonometry:

Understanding trigonometric identities facilitates vector analysis, enhancing your grasp of forces, velocities, and directions.

Higher-order Problem Solving:

The chapter sharpens your analytical thinking, enabling you to dissect complex scenarios, especially in coordinate geometry and calculus.

Geometric Insight:

Trigonometry unveils spatial relationships, aiding in angle calculations, navigation, and understanding geometric shapes.

Precursor to Advanced Topics:

Trigonometry serves as a foundation for calculus, complex numbers, and further mathematical studies.

Formula-Memory Connection: Strengthening Knowledge with Revision Notes

Equations are more than just symbols –They're your secret code to solve problems in Maths. When you understand formulas, you can easily handle tricky ideas and feel more sure of yourself.  Use the equation with JEE Main Maths Revision notes to improve studying. Check out our JEE Main Maths formula pages and begin your journey to prepare for JEE Main now!

Check few of the important Formulas needed for JEE Main exam preparation:

Basic Trigonometric Ratios

1. $\sin \theta = \frac{\text{Opposite Side}}{\text{Hypotenuse}}$

2. $\cos \theta = \frac{\text{Adjacent Side}}{\text{Hypotenuse}}$

3. $\tan \theta = \frac{\text{Opposite Side}}{\text{Adjacent Side}} = \frac{\sin \theta}{\cos \theta}$

Reciprocal Identities

1. $\csc \theta = \frac{1}{\sin \theta}$

2. $\sec \theta = \frac{1}{\cos \theta}$

3. $\cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta}$

Pythagorean Identities

1. $\sin^2 \theta + \cos^2 \theta = 1$

2. $1 + \tan^2 \theta = \sec^2 \theta$

3. $1 + \cot^2 \theta = \csc^2 \theta$

Angle Sum and Difference Identities

1. $\sin (A \pm B) = \sin A \cos B \pm \cos A \sin B$

2. $\cos (A \pm B) = \cos A \cos B \mp \sin A \sin B$

3. $\tan (A \pm B) = \frac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$

Double Angle Identities

1. $\sin 2A = 2 \sin A \cos A$

2. $\cos 2A = \cos^2 A - \sin^2 A = 2 \cos^2 A - 1 = 1 - 2 \sin^2 A$

3. $\tan 2A = \frac{2 \tan A}{1 - \tan^2 A}$

Half-Angle Identities

1. $\sin \frac{A}{2} = \pm \sqrt{\frac{1 - \cos A}{2}}$

2. $\cos \frac{A}{2} = \pm \sqrt{\frac{1 + \cos A}{2}}$

3. $\tan \frac{A}{2} = \pm \sqrt{\frac{1 - \cos A}{1 + \cos A}} = \frac{\sin A}{1 + \cos A} = \frac{1 - \cos A}{\sin A}$

Product-to-Sum Identities

1. $\sin A \sin B = \frac{1}{2} [\cos (A - B) - \cos (A + B)]$

2. $\cos A \cos B = \frac{1}{2} [\cos (A + B) + \cos (A - B)]$

3. $\sin A \cos B = \frac{1}{2} [\sin (A + B) + \sin (A - B)]$

Sum-to-Product Identities

1. $\sin A + \sin B = 2 \sin \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right)$

2. $\sin A - \sin B = 2 \cos \left( \frac{A + B}{2} \right) \sin \left( \frac{A - B}{2} \right)$

3. $\cos A + \cos B = 2 \cos \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right)$

4. $\cos A - \cos B = -2 \sin \left( \frac{A + B}{2} \right) \sin \left( \frac{A - B}{2} \right)$

Trigonometric Values of Standard Angles

1. $\sin 0^\circ = 0$, $\sin 30^\circ = \dfrac{1}{2}$, $\sin 45^\circ = \dfrac{1}{\sqrt{2}}$, $\sin 60^\circ = \dfrac{\sqrt{3}}{2}$, $\sin 90^\circ = 1$

2. $\cos 0^\circ = 1$, $\cos 30^\circ = \dfrac{\sqrt{3}}{2}$, $\cos 45^\circ = \frac{1}{\sqrt{2}}$, $\cos 60^\circ = \dfrac{1}{2}$, $\cos 90^\circ = 0$

3. $\tan 0^\circ = 0$, $\tan 30^\circ = \dfrac{1}{\sqrt{3}}$, $\tan 45^\circ = 1$, $\tan 60^\circ = \sqrt{3}$, $\tan 90^\circ$ is undefined. 

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Enhance your Results with Vedantu’s JEE Main Notes

As you work hard to do well in JEE Main 2025, think of Trigonometry Notes as your helpful friend. They simplify hard things, show what's important, and let you practise, which improves your study. Vedantu's JEE Main notes help you and you'll understand things, solve problems without fear, and do well in the exam. Get the Trigonometry Revision Notes for FREE to improve and succeed in JEE Main 2025.