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A student writes \(\sin^{-1}(\sin(5\pi/6))=5\pi/6\). What is the correct correction to this error?एक विद्यार्थी ने लिखा: \(\sin^{-1}(\sin(5\pi/6))=5\pi/6\)। उसकी गलती का सही सुधार क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\sin^{-1}(\sin(5\pi/6))=\pi/6\) because the principal value of \(\sin^{-1}\) lies in \([-\pi/2,\pi/2]\)\(\sin^{-1}(\sin(5\pi/6))=\pi/6\) क्योंकि \(\sin^{-1}\) का प्रमुख मान \([-\pi/2,\pi/2]\) में होता है
Since \(\sin(5\pi/6)=1/2\), we need the angle in the principal range \([-\pi/2,\pi/2]\) whose sine is \(1/2\). It is \(\pi/6\), not \(5\pi/6\). Exam tip: always check the principal-value range first.\(\sin(5\pi/6)=1/2\) और \(\sin^{-1}\) का प्रमुख मान \([-\pi/2,\pi/2]\) में लिया जाता है। इसलिए \(\sin^{-1}(1/2)=\pi/6\), न कि \(5\pi/6\)। परीक्षा टिप: पहले कोण को प्रमुख मान-परास में जाँचें।
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