How do you find the exact value of ${sin}^{- 1} [sin (- \frac{π}{10})]$ $sin^-1[sin(-pi/10)]$ ?

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How do you find the exact value of ${sin}^{- 1} [sin (- \frac{π}{10})]$ $sin^-1[sin(-pi/10)]$ ?

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Answer 1 · 2015-07-03T20:06:40

${sin}^{- 1} [sin (- \frac{π}{10})] = - \frac{π}{10}$ $sin^-1[sin(-pi/10)]=-pi/10$

Explanation:

${sin}^{- 1} [sin (- \frac{π}{10})]$ $sin^-1[sin(-pi/10)]$

A simple way to understand this is from the fact that: ${sin}^{- 1}$ $color(green)(sin^-1)$ (also denoted byt $arcsin$ $color(green)arcsin$ ) is the inverse trig function of $sin$ $color(green)sin$

So if you $sin$ $sin$ an angle, you get an real number that lies between $- 1$ $-1$ and $1$ $1$

On the other hand if you ${sin}^{- 1}$ $sin^-1$ the answer got previously, you get back the angle.

In the present case, let's say you originally had the angle $- \frac{π}{10}$ $-pi/10$

Now, you when you $sin$ $color(red)sin$ it you obtain $sin (- \frac{π}{10})$ $sin(-pi/10)$

Then, if you ${sin}^{- 1}$ $color(red)(sin^-1)$ it this time you will get back the angle: $- \frac{π}{10}$ $-pi/10$

That is ${sin}^{- 1}$ $sin^-1$ of $sin (- \frac{π}{10})$ $sin(-pi/10)$ is $- \frac{π}{10}$ $-pi/10$

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How do you find the exact value of ${sin}^{- 1} [sin (- \frac{π}{10})]$ $sin^-1[sin(-pi/10)]$ ?

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Explanation:

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How do you find the exact value of sin^-1[sin(-pi/10)]sin−1[sin(−π10)]sin^-1[sin(-pi/10)]?

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How do you find the exact value of ${sin}^{- 1} [sin (- \frac{π}{10})]$ $sin^-1[sin(-pi/10)]$ ?