Example 6 - Chapter 2 Class 12 Inverse Trigonometric Functions
Last updated at Dec. 16, 2024 by Teachoo
Finding principal value
Principal Value
You are here
You are here
Chapter 2 Class 12 Inverse Trigonometric Functions
Concept wise
Transcript
Example 6 Find the value of sin−1 (sin 3π/5) Let y = sin−1 ("sin " 3π/5) sin y = sin (3π/5) sin y = sin (108°) But, Range of sin−1 is [(−π)/2, π/2] i.e. [−90° ,90° ] Hence, y = 108° not possible Now, sin y = sin (108°) sin y = sin (180° – 72°) sin y = sin (72°) sin y = sin 𝟐𝝅/𝟓 Hence, y = 2𝜋/5 Which is in the range of sin-1 i.e. [(−π)/2, π/2] Hence, sin-1("sin " 3π/5) = y = 𝟐𝝅/𝟓
