sin-cos-1-3-2-

Question Number 59326 by prattushdas7@gmail.com last updated on 08/May/19

s i n {c o s}^{- 1} (- \sqrt{3 / 2)}

Commented by MJS last updated on 08/May/19

\sin \cos^{- 1} x = \cos \sin^{- 1} x = \sqrt{1 - x^{2}}

\sin \tan^{- 1} x = \frac{x}{\sqrt{1 + x^{2}}}

\cos \tan^{- 1} x = \frac{1}{\sqrt{1 + x^{2}}}

\tan \sin^{- 1} x = \frac{x}{\sqrt{1 - x^{2}}}

\tan \cos^{- 1} x = \frac{\sqrt{1 - x^{2}}}{x}

Answered by tanmay last updated on 08/May/19

\frac{3}{2} = 1.5

\sqrt{1.5} \approx 1.22

1 ⩾ c o s θ ⩾ - 1

s o q u e s t i o n i s

{s i n c o s}^{- 1} (\frac{- \sqrt{3}}{2})

= {s i n c o s}^{- 1} (- c o s \frac{π}{6})

= {s i n c o s}^{- 1} [c o s (π - \frac{π}{6})]

= s i n (π - \frac{π}{6})

= s i n \frac{π}{6}

= \frac{1}{2}

o r

{s i n c o s}^{- 1} (\frac{- \sqrt{3}}{2})

c o s a = \frac{- \sqrt{3}}{2} \to {c o s}^{2} a = \frac{3}{4}

{s i n}^{2} a = 1 - \frac{3}{4} = \frac{1}{4}

s i n a = \frac{1}{2}

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