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

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Transcript

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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.