Class 11 Mathematics — Chapter 3: TRIGONOMETRIC FUNCTIONS

Chapter 3: TRIGONOMETRIC FUNCTIONS is a chapter in Class 11 Mathematics (NCERT), part of the CBSE NCERT curriculum followed by over 25 million students across India. This chapter covers 7 topics including Angle Measurement Concepts, Degree Measure System, Radian Measure System. BrainWeave provides free AI-powered explanations — by voice or text, in Hindi or English — with no signup required.

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What you'll learn

▸Angle Measurement ConceptsCore concept

angleinitial sideterminal sidepositive anglenegative angle
▸Degree Measure SystemCore concept

degreeminutesecondrevolution360°
▸Radian Measure SystemCore concept

radianunit circlearc lengthsubtended anglel = rθ
▸Relationship between Degrees and RadiansCore concept

π radians180 degreesconversiondegree to radianradian to degree
▸Conversion from Degrees to RadiansCore concept

convert degreesπ/180degree measureminutes to degreesradian measure
▸Conversion from Radians to DegreesCore concept

convert radians180/πradian measuredegree measuredegree-minute-second
▸Applications of the Arc Length Formula

arc lengthradiuscentral angleword problemspendulum

Chapter Summary

Understanding the definition of an angle as a measure of rotation, including the initial side, terminal side, vertex, and the convention for positive (anticlockwise) and negative (clockwise) angles.

Understanding the system of measuring angles in degrees, where one full revolution is 360°. This includes the subdivisions of a degree into 60 minutes (1° = 60') and a minute into 60 seconds (1' = 60'').

Understanding the definition of a radian as the angle subtended at the center of a unit circle by an arc of length 1 unit. This includes the general relationship between arc length (l), radius (r), and the central angle in radians (θ), given by the formula l = rθ.

Mastering the fundamental conversion relationship between the two angle measurement systems: π radians = 180°. Students should know the radian equivalents of common angles like 30°, 45°, 60°, 90°, 180°, and 360°.

Applying the formula to convert angles from degree measure to radian measure. This includes converting angles given in a degrees-minutes format (e.g., 40° 20') into a single radian value.

Applying the formula to convert angles from radian measure to degree measure. This includes converting a single radian value into the degrees, minutes, and seconds format.

Solving practical problems involving circles, such as finding the radius, arc length, or central angle using the formula l = rθ. This requires ensuring the angle is always in radians before using the formula.

Practice Questions from this Chapter

Tap "Get Solution" on any question to ask our AI tutor.

Show a real-world use of radians. Get Solution →
Explain trigonometry's oldest known use. Get Solution →
Give examples of positive and negative angles. Get Solution →
According to the text, what is the direction of rotation for an angle to be considered positive? Get Solution →
How many minutes (') are in one degree (°)? Get Solution →
What is the fundamental relationship between π radians and degrees? Get Solution →
In the context of a unit circle where a point P(a, b) corresponds to an angle x, how is cos x defined? Get Solution →
According to the table of values for quadrantal angles, what is the value of sin(0°)? Get Solution →

Did you know?

💡 Ancient Babylonians divided a circle into 360 degrees, influencing math today.
💡 Sailors navigated vast oceans for centuries using trigonometry and star positions.
💡 Bees communicate nectar locations using precise angles in their waggle dance.
💡 Trigonometry helps describe musical sounds, ocean tides, and even atoms.
💡 Your eyes use trigonometric calculations to estimate distances and depths.

Frequently Asked Questions

How many topics are covered in this chapter?

This chapter covers 7 key topics: Angle Measurement Concepts, Degree Measure System, Radian Measure System, Relationship between Degrees and Radians, Conversion from Degrees to Radians, and more. The BrainWeave AI tutor explains each one with examples.

Is Chapter 3: TRIGONOMETRIC FUNCTIONS important for board exams?

Class 11 is a foundation year. Mastering this chapter now will help you build strong fundamentals for the higher classes.

Can I get NCERT solutions for this chapter in Hindi?

Yes. BrainWeave's AI tutor supports Hindi, English, and Hinglish for both voice and text chat. Just ask your question in your preferred language.

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Related Chapters

Chapter 2: RELATIONS AND FUNCTIONS

Chapter 4: COMPLEX NUMBERS AND QUADRATIC EQUATIONS

Chapter 1: SETS

Chapter 13: STATISTICS

Chapter 14: PROBABILITY

Chapter 9: STRAIGHT LINES

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