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Find the principal value of \begin{align} sin^{-1}\left(-\frac{1}{2}\r...

Find the principal value of egin{align | Class 12 Mathematics Chapter Inverse Trigonometric Functions, Inverse Trigonometric Functions NCERT Solutions

Question: Find the principal value of \begin{align} sin^{-1}\left(-\frac{1}{2}\right)\end{align}

Answer:

\begin{align} sin^{-1}\left(-\frac{1}{2}\right)=y \;\;Then\;\; sin y = -\frac{1}{2} = -sin\left(\frac{\pi}{6}\right)= sin\left(-\frac{\pi}{6}\right)\end{align}

We know that the range of the principal value branch of sin⁻¹ is

\begin{align} \left[-\frac{\pi}{2},\frac{\pi}{2}\right] and \;\;sin\left(-\frac{\pi}{6}\right) = -\frac{1}{2}\end{align}

Therefore, the principal value of

\begin{align} sin^{-1}\left(-\frac{1}{2}\right) is -\frac{\pi}{6}\end{align}

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Popular questions of class 12 Mathematics

Q: Given an example of a relation. Which is
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Read the question carefully and focus on the core concept being asked.
Reference examples and data from the chapter when answering questions about Inverse Trigonometric Functions.
Review previous year question papers to get an idea of how such questions may be framed in exams.
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Discuss your answers with your teachers or peers to get feedback and improve your understanding.

Comments

Ankit Kumar
2019-05-17 20:53:35

Why not show full solutions?

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Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 1 , Question 1: Find the principal value of egin{align} sin^{-1}left(-frac{1}{2} ight)end{align}....

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Find the principal value of egin{align | Class 12 Mathematics Chapter Inverse Trigonometric Functions, Inverse Trigonometric Functions NCERT Solutions