How do you calculate the ${sin}^{- 1} (.6075)$ $sin ^ -1 (.6075)$ ?

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How do you calculate the ${sin}^{- 1} (.6075)$ $sin ^ -1 (.6075)$ ?

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Answer 1 · 2015-11-29T21:34:44

$θ = {37.41}^{\circ}, {142.59}^{\circ}$ $theta=37.41^@, 142.59^@$

Explanation:

Since $0.6075$ $0.6075$ is not an angle in a special triangle, we have to use a calculator:

$sin θ = (0.6075)$ $sintheta=(0.6075)$
$θ = {sin}^{- 1} (0.6075)$ $theta=sin^-1(0.6075)$
$θ \approx {37.41}^{\circ}$ $theta~~37.41^@$

However, since the CAST rule states that sine is positive in quadrants $1$ $1$ and $2$ $2$ , our answer should also include the other principal angle in quadrant $2$ $2$ .

To find the other angle, we do $180^{\circ} - {37.41}^{\circ}$ $180^@-37.41^@$ to find the principal angle in quadrant $2$ $2$ :

$180^{\circ} - {37.41}^{\circ}$ $180^@-37.41^@$
$\approx {142.59}^{\circ}$ $~~142.59^@$

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How do you calculate the ${sin}^{- 1} (.6075)$ $sin ^ -1 (.6075)$ ?

1 Answer

Explanation:

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