Trigonometry Class 11 Notes: Formulas, Equations and JEE Tips

 Trigonometry is the base for calculus, vectors and coordinate geometry. These Trigonometry Class 11 notes explain the chapter in order, from angles to equations. For the complete list of formulas, keep the trigonometry formula page open as your quick-reference sheet.

Trigonometry Class 11 Notes: Syllabus and Chapter Overview

The topics in these Trigonometry Class 11 notes follow NCERT Chapter 3 and the CBSE 2026-27 course. In that course, Trigonometric Functions comes under Unit I (Sets and Functions). The topics are:

• positive and negative angles
• measuring angles in radians and degrees
• the unit-circle definition of trigonometric functions
• signs, domain, range and graphs
• sum and difference formulas, with related identities
• general solutions of equations of the type $\sin y=\sin a$, $\cos y=\cos a$ and $\tan y=\tan a$

JEE Main goes further with multiple-angle and transformation identities and harder equations. Check the official CBSE curriculum for any change.

Visual Notes on Trigonometric Equations

These pages from eSaral’s handwritten notes cover trigonometric equations with solved questions.

India's Best Exam Preparation for Class 11th - Download Now

India's Best Exam Preparation for Class 11th - Download Now

India's Best Exam Preparation for Class 11th - Download Now

India's Best Exam Preparation for Class 11th - Download Now

India's Best Exam Preparation for Class 11th - Download Now

Angles and Radian Measure in Trigonometry Class 11 Notes

Radian measure is the first idea to master in Trigonometry Class 11 notes, because later formulas and graphs use angles in radians. One radian is the angle at the centre of a circle that cuts off an arc equal in length to the radius. The key relation is $\pi$ radians $=180^\circ$. For arc length $l$ on a circle of radius $r$ with angle $\theta$ in radians:

$$l=r\theta$$

How to Convert Degrees to Radians

$$\text{Radians}=\frac{\pi}{180}\times\text{Degrees},\qquad \text{Degrees}=\frac{180}{\pi}\times\text{Radians}$$

For example, $75^\circ=\dfrac{75\pi}{180}=\dfrac{5\pi}{12}$ radians.

Trigonometric Ratios of Standard Angles

Learn this table first, because most Trigonometry Class 11 notes and problems use these values.

Signs and Domain-Range of Trigonometric Functions in Class 11

Signs by quadrant: In the first quadrant all ratios are positive. In the second only $\sin$ and $\csc$ are positive. In the third only $\tan$ and $\cot$. In the fourth only $\cos$ and $\sec$.

Here $n\in\mathbb{Z}$. The functions $\sin$ and $\cos$ have period $2\pi$, and $\tan$ and $\cot$ have period $\pi$.

Trigonometric Identities in Trigonometry Class 11 Notes

Pythagorean Identities

$$\sin^2\theta+\cos^2\theta=1,\qquad 1+\tan^2\theta=\sec^2\theta,\qquad 1+\cot^2\theta=\csc^2\theta$$

Sum and Difference Formulas

$$\sin(A\pm B)=\sin A\cos B\pm\cos A\sin B$$ $$\cos(A\pm B)=\cos A\cos B\mp\sin A\sin B$$ $$\tan(A\pm B)=\frac{\tan A\pm\tan B}{1\mp\tan A\tan B}$$

Double and Triple Angle Formulas

$$\sin 2A=2\sin A\cos A$$ $$\cos 2A=\cos^2A-\sin^2A=2\cos^2A-1=1-2\sin^2A$$ $$\tan 2A=\frac{2\tan A}{1-\tan^2A}$$ $$\sin 3A=3\sin A-4\sin^3A,\qquad \cos 3A=4\cos^3A-3\cos A$$

The triple-angle and transformation formulas are mainly for JEE. The sum formulas are the base from which the others can be derived.

Trigonometric Equations in Trigonometry Class 11 Notes: General Solutions

A trigonometric equation is true only for particular values of the angle. Because the functions are periodic, Trigonometry Class 11 notes write all solutions with an integer $n$.

Steps to Solve a Trigonometric Equation

1. Reduce the equation to a single trigonometric function if possible.
2. Factorise instead of cancelling a common factor.
3. Write the general solution for each factor.
4. Check that the solutions do not make $\tan$, $\sec$, $\cot$ or $\csc$ undefined.

Solved Examples on Trigonometry Class 11 Notes

Example 1. Find $\sin 75^\circ$.

$$\sin 75^\circ=\sin(45^\circ+30^\circ)=\frac{1}{\sqrt{2}}\cdot\frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\cdot\frac{1}{2}=\frac{\sqrt{3}+1}{2\sqrt{2}}=\frac{\sqrt{6}+\sqrt{2}}{4}$$

Example 2. Solve $2\sin\theta-1=0$.

$\sin\theta=\dfrac{1}{2}=\sin\dfrac{\pi}{6}$, so $\theta=n\pi+(-1)^n\dfrac{\pi}{6}$, $n\in\mathbb{Z}$. This covers both $\dfrac{\pi}{6}+2n\pi$ and $\dfrac{5\pi}{6}+2n\pi$.

Example 3. Solve $\cos 2\theta=\dfrac{1}{2}$.

$\cos 2\theta=\cos\dfrac{\pi}{3}$, so $2\theta=2n\pi\pm\dfrac{\pi}{3}$ and $\theta=n\pi\pm\dfrac{\pi}{6}$.

Example 4. Solve $\tan 3\theta=\tan\theta$.

$3\theta=n\pi+\theta$, so $\theta=\dfrac{n\pi}{2}$. For odd $n$, $\tan\theta$ is undefined, so those values are rejected. The solution is $\theta=n\pi$.

Example 5. Solve $2\sin^2\theta+\sin\theta-1=0$.

Factorise: $(2\sin\theta-1)(\sin\theta+1)=0$. So $\sin\theta=\dfrac{1}{2}$, which gives $\theta=n\pi+(-1)^n\dfrac{\pi}{6}$, or $\sin\theta=-1$, which gives $\theta=2n\pi-\dfrac{\pi}{2}$.

Common Mistakes in Trigonometry Class 11 Notes

• Writing $\theta=n\pi\pm\alpha$ for $\sin\theta=\sin\alpha$ and leaving out the $(-1)^n$ factor.
• Not rejecting values that make a function undefined, as in Example 4.
• Cancelling a common factor such as $\sin\theta$ and losing roots, instead of factorising.
• Using degrees in $l=r\theta$. The angle must be in radians.
• Squaring both sides and keeping extra roots without checking them.

Trigonometry Class 11 Notes for JEE Main

• Derive, don’t memorise. Most identities come from the sum and difference formulas.
• Practise general solutions. Equation questions test the $(-1)^n$ form, domain checks and factorisation.
• Carry the skills forward. Trigonometric substitution is used in calculus and coordinate geometry.
• Test yourself. Try questions from JEE Main chapterwise PYQs after finishing the theory.

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These notes explain the concepts — pair them with the trigonometry formula page as your quick-reference sheet for the formulas themselves.