4.5.3 The inverse tangent function and its properties
Chapter 4: Chapter 4 · MATHEMATICS-VOLUME 1 · EN medium
From your actual textbook ✓
What does your textbook say about 4.5.3 The inverse tangent function and its properties?
. . The inverse tangent function and its properties The tangent function is not one-to-one in the entire domain \ + ∈ . However, : → is a bijective function. Now, we define the inverse tangent function with as its domain and − as its range. Definition . For any real number x , define tan - x as the unique number y in − such that tan In other words, the inverse tangent function tan : −∞∞ ) →− is defined by tan ( ) x if and only if tan y and y ∈− From the definition of y tan , we observe the following: (i) y tan if and only if x = tan for x ∈ and − < < (ii) tan tan −
📖 Class 12 Mathematics English Volume 1 2025 Edition www.tntextbooks.in · Page 153
Read from the source
Complete lesson
. . The inverse tangent function and its properties The tangent function is not one-to-one in the entire domain \ + ∈ . However, : → is a bijective function.
Now, we define the inverse tangent function with as its domain and − as its range. Definition . For any real number x , define tan - x as the unique number y in − such that tan In other words, the inverse tangent function tan : −∞∞ ) →− is defined by tan ( ) x if and only if tan y and y ∈− From the definition of y tan , we observe the following: (i) y tan if and only if x = tan for x ∈ and − < < (ii) tan tan −
Related topics
Want this shaped for your exam marks?
Get an AI answer grounded in your actual textbook — with the exact page reference.
Ask AI about this topic →