exercise - 2.1 🤯| chapter - 2 | inverse trigonometric functions 🔥| class 12 #inversetrigonometry

exercise - 2.1 🤯| chapter - 2 | inverse trigonometric functions 🔥| class 12 #inversetrigonometry inverse trigonometric functions, class 12 chapter 3 solutions, how to find values of angles of sin cos tan cosec sec and cot, values of sin cos tan, exercise - 2.1, domain of sin inverse cos inverse tan inverse, range of sin inverse cos inverse tan inverse, range of trigonometric functions, domain of trigonometric functions, range of inverse trigonometric functions, domain of inverse trigonometric functions, maths by faiz sir, infinix classes, infinix classes faiz sir, infinix classes gopalganj, class 12 maths, class 12 chapter 3 maths, class 12 maths, range of tan theta, range of sin theta, range of cos theta, range of sec theta, range of cosec theta, range of cot theta, domain of sin theta, domain of cos theta, domain of tan theta, domain of sec theta, domain of cosec theta, domain of cot theta, find the principal values, find the value of tan theta, sin theta, cos theta, find the principal value of sin theta, find the principal value of cos theta, find the principal value of tan theta, #trigonometry #trigonometricfunctions #inversetrigonometryfunction #inversetrigonometricfunctionsclass12 #inversetrigonometricfunction #inversetrigonometricfunctions #inversetrigonometry #class12thncertmathchapter1 #class12thmathsdoubt #class_12_maths #class_12_math_solution #maths_concept #maths_tricks #mathsbyfaizsir #infinixclasses #faizsir #codomain #domain #range #viralpost #exercise2b #mathswallah Find the principal values of the following: 1. sin–1 (−𝟏/𝟐) 2. cos–1 (√𝟑/𝟐) 3. cosec–1 (2) 4. tan–1 (-√3) 5. cos–1(-1/2) 6. tan–1 (–1) 7. sec–1 (𝟐/√𝟑) 8. cot–1 (√3) 9. cos–1 (−𝟏/√𝟐) 10. cosec–1 (-√2) Find the values of the following: 11. tan–1(1) + cos–1 (-1/2) + sin–1 (-1/2) 12. cos–1 (1/2) + 2 sin–1 (1/2) 13. If sin–1 x = y, then (A) 0 less than equal to y less than equal to π (B) – π/2 less than equal to y less than equal to π/2 (C) 0 less than y less than π (D) – π/2 less than y less than π/2 14. tan–1 √𝟑 − sec-1 (-2) is equal to (A) π (B) − π /3 (C) π/3 (D) 2 π/3 Inverse trigonometric functions, also known as inverse circular functions or arc functions, are the inverses of standard trigonometric functions (sine, cosine, tangent, etc.). They are used to find the angle of a triangle given a trigonometric ratio. For example, arcsin(x) finds the angle whose sine is x. Key Concepts: Inverse Functions: An inverse function "undoes" the original function. If y = f(x), then the inverse is x = f⁻¹(y). Principal Values: To make inverse trigonometric functions one-to-one, their domain is restricted to specific intervals, and the corresponding range is called the principal value. Notations: Inverse trigonometric functions are often written as arcsin(x), arccos(x), arctan(x), etc., or with the exponent notation like sin⁻¹(x), cos⁻¹(x), tan⁻¹(x). Domain and Range: arcsin(x) and arctan(x): Domain: -1 less than equal to x less than equal to 1, Range: -π/2 less than equal to y less than equal to π/2 arccos(x): Domain: -1 less than equal to x less than equal to 1, Range: 0 less than equal to y less than equal to π cot⁻¹(x): Domain: All real numbers, Range: 0 less tha y less than π sec⁻¹(x): Domain: x less than equal to -1 or x greater than equal to 1, Range: 0 less than equal to y less than equal to π, y ≠ π/2 csc⁻¹(x): Domain: x less than equal to -1 or x greater than equal to 1, Range: -π/2 less than equal to y less than equal to π/2, y ≠ 0 Common Formulas and Identities: sin⁻¹(sin(y)) = y if -π/2 less than equal to y less than equal to π/2 cos⁻¹(cos(y)) = y if 0 less than equal to y less than equal to π tan⁻¹(tan(y)) = y if -π/2 less than y less than π/2 sin⁻¹(-x) = -sin⁻¹(x) cos⁻¹(-x) = π - cos⁻¹(x) tan⁻¹(-x) = -tan⁻¹(x) Example: To find the angle whose sine is 0.5, you would use arcsin(0.5), which would return π/6 (or 30 degrees).