Question

find the value of sin^-1 (-1/2)​

Answer 1

Answer:

-π/6

Step-by-step explanation:

y = sin^-1(-1/2)

y = sin^-1(sin (-π/6))

y = -π/6

Hence, Principal value of sin^-1 (-1/2) is -π/6.

Note: Range of sin^-1 is [-π/2,π/2]

Answer 2

Step-by-step explanation:

$\mathtt{ \:let \: y = {sin}^{ - 1} ( \frac{1}{2})}$

$\mathtt{sin \: y = - \frac{1}{2} }$

$\mathtt{ \: sin \: y = \sin( \frac{\pi}{6} ) }$

${\mathtt { \underline{\red{the \: range \: of \: principal \: value \: of \: {sin}^{ - 1} \: is \: between \: - \frac{\pi}{2} \: and \: \frac{\pi}{2} . }}}}$

$\boxed {\mathtt \pink{hence \: the \: principal \: value \: is \: - \frac{\pi}{6}. }}$

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