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Find the approximate value of ^{-1}(0.51) given that {3}=1.73

Question

Find the approximate value of $sin^{- 1} (0.51)$ given that $3 = 1.7321$

\frac{π}{6} + 0.011541

\frac{π}{3} + 0.011541

\frac{π}{6} + 0.011547

\frac{π}{3} + 0.011547

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Emma Discussed

Find the approximate value of

sin^{- 1} (0.51)

given that

3 = 1.7321

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

sin^{- 1} (0.5 + 0.01) = sin^{1} (0.51)

∴

Approx value

= f (x) + h f ’ (x)

Here

x = 0.5

h = 0.01

f (u) = sin^{1} x

f ‘ (u) = \frac{1}{1 - x ^{2}}

∴ f (0.5) = sin^{- 1} (0.5) = \frac{π}{6}

∴ f ’ (0.5) = \frac{1}{1 - ( 0.5 ) ^{2}}

= \frac{1}{0.75}

= \frac{2}{3}

∴

Approx value

= \frac{π}{6} + \frac{2}{3} \times (\frac{1}{100})

\frac{π}{6} + \frac{2}{100 3}

= \frac{π}{6} + 0.011541

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Question Text	Find the approximate value of $sin^{- 1} (0.51)$ given that $3 = 1.7321$
Answer Type	Text solution:1
Upvotes	150