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Find the value of sin -1  [sin(13π/7)]



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Question 21 (Choice 1) Find the value of 〖𝑠𝑖𝑛〗^(βˆ’1) [𝑠𝑖𝑛(13πœ‹/7)]. Let y = sinβˆ’1 ("sin " 13Ο€/7) sin y = sin (13Ο€/7) sin y = sin (334Β°) But, Range of sinβˆ’1 is [(βˆ’Ο€)/2, Ο€/2] i.e. [βˆ’90Β° ,90Β° ] Hence, y = 334Β° not possible Now, sin y = sin (13Ο€/7) sin y = sin (πŸπ…βˆ’π›‘/πŸ•) sin y = βˆ’ sin (𝛑/πŸ•) sin y = sin ((βˆ’π›‘)/πŸ•) Hence, y = (βˆ’π…)/πŸ• Which is in the range of sin-1 i.e. [(βˆ’Ο€)/2, Ο€/2] Hence, sin-1("sin " 13Ο€/7) = y = (βˆ’π…)/πŸ•

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.