Example 9 - Chapter 2 Inverse trigonometry - Find sin-1 (sin

Example 9 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2

  1. Chapter 2 Class 12 Inverse Trigonometric Functions (Term 1)
  2. Serial order wise

Transcript

Example 9 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

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.