Trigonometric Functions Chapter 3 Class 11 Maths Online Practice Worksheet

Trigonometric Functions Class 11 Mathematics — Complete Worksheet Practice Guide

This DigiSadhan Class 11 Mathematics practice tool is designed for Chapter 3, Trigonometric Functions. It provides structured revision of angle measurement, degree-radian conversion, trigonometric functions, signs in different quadrants, standard values, identities, allied angles, graphs, domains, ranges and periodicity. Use it with your prescribed NCERT textbook and classroom teaching. The requested NCERT page is the official textbook-access page for the Class 11 Mathematics material. citeturn0view0

1. Angle Measurement

Angles can be measured in degrees and radians. A complete revolution is 360° or 2π radians. The radian measure is especially important in higher mathematics because it connects angle measurement naturally with the circumference of a circle.

180° = π radians; 360° = 2π radians; 1° = π/180 rad; 1 rad = 180°/π.

2. Degree to Radian Conversion

To convert degrees into radians, multiply the degree value by π/180. To convert radians into degrees, multiply by 180/π. Students should practise standard angles such as 30°, 45°, 60°, 90°, 180° and their radian equivalents.

θ° × π/180 = θ radians; θ rad × 180/π = θ°.

3. Trigonometric Functions

For an angle θ, the six fundamental trigonometric functions are sine, cosine, tangent, cosecant, secant and cotangent. In a right-triangle setting, their ratios relate the sides to the chosen angle. In a general setting, the unit-circle definition extends these functions to all real angles.

tan θ = sin θ / cos θ; cot θ = cos θ / sin θ; sec θ = 1/cos θ; cosec θ = 1/sin θ.

4. Unit Circle Idea

On the unit circle, a point corresponding to angle θ has coordinates (cos θ, sin θ). This gives a powerful geometric interpretation of sine and cosine and explains their values for angles beyond a single right triangle.

5. Signs in Four Quadrants

The signs of trigonometric functions depend on the quadrant. In the first quadrant, sine, cosine and tangent are positive. In the second quadrant sine is positive while cosine and tangent are negative. In the third quadrant tangent is positive while sine and cosine are negative. In the fourth quadrant cosine is positive while sine and tangent are negative.

QI: all positive • QII: sin positive • QIII: tan positive • QIV: cos positive.

6. Standard Trigonometric Values

Memorising the standard values for 0°, 30°, 45°, 60° and 90° is useful for fast evaluation. The same values can be extended to related angles using signs and reference angles.

sin 0°=0, sin 30°=1/2, sin 45°=1/√2, sin 60°=√3/2, sin 90°=1.

cos 0°=1, cos 30°=√3/2, cos 45°=1/√2, cos 60°=1/2, cos 90°=0.

7. Fundamental Identities

Trigonometric identities are equations true for all values for which both sides are defined. The three basic Pythagorean identities form the foundation for simplification and proof questions.

sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.

8. Reciprocal and Quotient Relationships

Reciprocal identities connect pairs of functions, while quotient identities connect tangent and cotangent with sine and cosine. Students should be comfortable converting an expression into the form most useful for a calculation.

sec θ=1/cos θ; cosec θ=1/sin θ; cot θ=1/tan θ; tan θ=sin θ/cos θ; cot θ=cos θ/sin θ.

9. Allied Angles

Angles related to 90°, 180°, 270° and 360° can be simplified by using reference-angle relationships and quadrant signs. For example, sine and cosine may change into each other when an angle is shifted by 90°, while a 180° shift changes the sign of sine and cosine.

sin(90°−θ)=cos θ; cos(90°−θ)=sin θ; sin(180°−θ)=sin θ; cos(180°−θ)=−cos θ.

10. Even and Odd Properties

Cosine is an even function, while sine and tangent are odd functions. These properties are useful when simplifying negative-angle expressions.

cos(−θ)=cos θ; sin(−θ)=−sin θ; tan(−θ)=−tan θ.

11. Periodicity

Trigonometric functions repeat their values after fixed intervals. Sine and cosine have period 2π, while tangent and cotangent have period π. Understanding periodicity is essential when analysing graphs and solving trigonometric expressions.

sin(θ+2π)=sin θ; cos(θ+2π)=cos θ; tan(θ+π)=tan θ.

12. Domains and Ranges

The domain and range describe which inputs and outputs are possible. Sine and cosine accept every real number and produce values between −1 and 1. Tangent is undefined wherever cosine is zero. Cosecant is undefined wherever sine is zero; secant is undefined wherever cosine is zero.

Domain(sin x)=R, Range(sin x)=[−1,1]; Domain(cos x)=R, Range(cos x)=[−1,1].

13. Graphs

The graphs of sine and cosine are periodic waves, while tangent has repeating branches with vertical asymptotes. Graph questions may ask about intercepts, maxima, minima, period, symmetry and undefined points. Recognising standard graph features makes many questions quicker.

14. Nine-plus Question Types

1 Degree/Radian2 Standard Values3 Signs & Quadrants4 Trig Ratios5 Identities6 Allied Angles7 Domains & Ranges8 Periodicity9 Graph Concepts10 Simplification

15. Difficulty Levels

Easy questions practise definitions, standard values and direct conversions. Medium questions combine values, signs, identities or angle relationships. Hard questions require multiple steps, identity manipulation, domain reasoning or periodicity. Mixed mode provides broad revision.

16. Randomized Worksheet Practice

The worksheet is randomized whenever a new test is started. The Shuffle Whole Worksheet control rearranges every question and independently randomizes multiple-choice choices. This prevents students from relying on a fixed answer position and makes repeated revision more effective.

17. Answer Checking and Feedback

Students must attempt each question before viewing its answer. After Check Answer, a correct response receives green styling and a positive animation and sound. A wrong response receives red styling and a different animation and sound. Show Answer is hidden until the checking step has occurred.

18. Timer, Progress and Score

Students may choose no timer or a 5, 10, 15 or 30-minute session. The progress bar records checked questions and the score counts correct responses. Once all questions are checked, the final result shows the score and percentage.

19. PDF and Print

The Save as PDF control is separate from Print. PDF generates a downloadable worksheet file, while Print uses the browser print facility. This provides both digital and paper-based practice options.

20. Mobile-Friendly Student Design

The interface is built mobile-first because many learners practise on smartphones. Controls wrap cleanly, answer options become a single column on small screens, and buttons are touch-friendly. Animated mathematical symbols provide engaging graphics for students without interfering with the learning content.

21. Smart Revision Strategy

Begin with degree-radian conversion and standard values. Then revise quadrant signs and reciprocal relationships. Next practise fundamental identities and allied angles. Finish with domains, ranges, graphs and periodicity. Use the difficulty selector to move from direct questions to multi-step problems. After checking mistakes, start a fresh shuffled test to confirm improvement.

Looking for a free Class 11 Trigonometric Functions online practice worksheet? DigiSadhan's Chapter 3 Maths worksheet helps students practise degree and radian conversion, standard trigonometric values, quadrants, identities, allied angles, domains, ranges, graphs and periodicity. With up to 2,000 questions, randomized worksheets and MCQ options, instant answer checking, progress tracking, optional timer, sound effects, animations, PDF download and print support, it is a powerful mobile-friendly revision tool for Class 11 students.