How do you evaluate ${arcsin}^{- 1} (- \frac{1}{2})$ $arcsin^-1(-1/2)$ without a calculator?

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How do you evaluate ${arcsin}^{- 1} (- \frac{1}{2})$ $arcsin^-1(-1/2)$ without a calculator?

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Answer 1 · 2018-05-25T17:37:54

$θ = \frac{11}{6} π = 330^{\circ}$ $theta = 11/6 pi = 330^@$

Explanation:

Given: ${arcsin}^{- 1} (- \frac{1}{2})$ $arcsin^-1 (-1/2)$

I believe what you want is $arcsin (- \frac{1}{2}) = {sin}^{- 1} (- \frac{1}{2})$ $arcsin (-1/2) = sin^-1(-1/2)$

$arcsin (- \frac{1}{2})$ $arcsin (-1/2)$ says, find me the angle that has a sine $= - \frac{1}{2}$ $= -1/2$ ,

or what is the angle $θ$ $theta$ that yields $sin θ = - \frac{1}{2}$ $sin theta = -1/2$ ?

Since the $arcsin$ $arcsin$ function has a limited domain: $- \frac{π}{2} \leq θ \leq \frac{π}{2}$ $-pi/2 <= theta <= pi/2$ , we will only need to look at the 4th quadrant due to the negative sign.

$θ = \frac{11}{6} π = 330^{\circ}$ $theta = 11/6 pi = 330^@$

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How do you evaluate ${arcsin}^{- 1} (- \frac{1}{2})$ $arcsin^-1(-1/2)$ without a calculator?

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How do you evaluate ${arcsin}^{- 1} (- \frac{1}{2})$ $arcsin^-1(-1/2)$ without a calculator?