# Trigonometric Functions Notes, Class 11 Mathematics | SwaVid Trigonometric Functions, NCERT Class 11 Mathematics: notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers. Canonical: https://www.swavid.com/cbse/class-11/maths/chapter/trigonometric-functions Source: https://www.swavid.com/cbse/class-11/maths/chapter/trigonometric-functions # Trigonometric Functions ## Formulas and definitions ## Key ideas ## Common mistakes ## Quick checks ## Keep going ## Questions parents ask ## Class 11 Mathematics on SwaVid ### Angles and radian measure ### Trigonometric functions on unit circle ### Signs and domain across quadrants ### Sum and difference identities ### Multiple and sub-multiple angle identities ### Next chapter ### Related chapter ### All chapters SwaVid › CBSE › Class 11 › Mathematics › Trigonometric Functions Notes written by SwaVid from the NCERT textbook. Class 11 Mathematics, Chapter 3. Key ideas, formulas and common mistakes. CBSE does not print marks for a single chapter. Short answer. This chapter extends trigonometric ratios from acute angles to real-valued functions defined on the unit circle using radian measure. Students learn the signs, graphs, and compound angle identities of trigonometric functions to evaluate expressions and simplify equations. Source: NCERT Mathematics (Reprint 2026-27) , Chapter 3, Trigonometric Functions An angle is generated by rotating a ray about its vertex. One radian is the angle subtended at the centre of a circle of radius r by an arc of length r, giving the relation l = r × θ, where π radians equals 180°. For a unit circle centered at the origin, a point P(a, b) at an angle x gives cos x = a and sin x = b. Since a² + b² = 1, it follows that cos² x + sin² x = 1 for any real number x. Sine is positive in quadrants I and II, cosine is positive in I and IV, and tangent is positive in I and III. Functions repeat their values after standard intervals, with sin x and cos x having a period of 2π, while tan x has a period of π. Identities express trigonometric values of (x ± y) in terms of functions of x and y, such as cos(x + y) = cos x cos y - sin x sin y. Related formulas yield expressions for functions of negative angles and complementary angles. Setting x = y leads to double-angle formulas for sin 2x, cos 2x, and tan 2x. Similar algebraic substitutions produce triple-angle formulas and formulas converting products of functions into sums or differences. Try each question first. Then tap it to see the answer. Degree measure = (Radian measure) × (180 / π) Degree measure = (7π / 6) × (180 / π) = 7 × 30 210° sin² x = 1 - cos² x = 1 - (-3/5)² = 1 - 9/25 = 16/25 In the third quadrant, sine is negative, so sin x = -√(16/25) -4/5 Write sin 15° as sin(45° - 30°) Use identity: sin(45° - 30°) = sin 45° cos 30° - cos 45° sin 30° Substitute values: (1 / √2) × (√3 / 2) - (1 / √2) × (1 / 2) = (√3 - 1) / (2√2) (√3 - 1) / (2√2) Complex Numbers and Quadratic Equations . Limits and Derivatives . The 14 chapters of Class 11 Mathematics . The CBSE Class 11 Maths curriculum says it gives no chapter or unit-wise weightage. Theory is 80 marks, plus 20 for internal assessment. No. They are written by SwaVid from the NCERT textbook. The CBSE curriculum is the reference for what is assessed. Complex Numbers and Quadratic Equations. SwaVid is an AI tutor for Indian students in Classes 6 to 12. It finds the earlier ideas a child missed, then teaches today’s chapter. Start free to see how it works. - Ch 3 NCERT book - 80 marks, theory paper - 3 quick checks - Using angles in degrees inside the formula l = r × θ . Always convert degree measures to radians before applying l = r × θ. - Writing cos(x + y) as cos x + cos y . Trigonometric operators do not distribute over addition; use the identity cos(x + y) = cos x cos y - sin x sin y. - Ignoring the quadrant sign when taking square roots . When calculating cos x = ±√(1 - sin² x), inspect the given quadrant of x to select either the positive or negative root. - Confusing the sign in cos x - cos y . Remember that cos x - cos y equals -2 sin((x + y) / 2) sin((x - y) / 2), keeping the negative sign in front. ## Key Links - [CBSE](https://www.swavid.com/cbse) - [Class 11](https://www.swavid.com/cbse/class-11) - [Mathematics](https://www.swavid.com/cbse/class-11/maths/chapters) - [Start free →](https://www.swavid.com/signup) - [All 14 chapters](https://www.swavid.com/cbse/class-11/maths/chapters) - [NCERT Mathematics (Reprint 2026-27)](https://ncert.nic.in/textbook.php) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/complex-numbers-and-quadratic-equations) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/limits-and-derivatives) - [Class 11 Mathematics](https://www.swavid.com/cbse/class-11/maths/chapters) - [Start free →](https://www.swavid.com/signup)