How do you calculate ${csc}^{- 1} (- 5)$ $csc^-1(-5)$ ?

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How do you calculate ${csc}^{- 1} (- 5)$ $csc^-1(-5)$ ?

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Answer 1 · 2015-11-23T04:28:48

$θ \approx {348.46}^{\circ}, {191.54}^{\circ}$ $theta~~348.46^@, 191.54^@$

Explanation:

${csc}^{- 1} (- 5)$ $csc^-1(-5)$

$csc θ = - 5$ $csctheta=-5$

$\frac{1}{sin θ} = - 5$ $1/sintheta=-5$

$sin θ = - \frac{1}{5}$ $sintheta=-1/5$

$θ = {sin}^{- 1} (- \frac{1}{5})$ $theta=sin^-1(-1/5)$

$θ \approx - {11.54}^{\circ} ({348.46}^{\circ})$ $theta~~-11.54^@ (348.46^@)$

However, since the CAST rule states that cosecant is also negative in quadrant $3$ $3$ , there is a second answer:

$θ = (360^{\circ} - {348.46}^{\circ}) + 180^{\circ}$ $theta=(360^@-348.46^@)+180^@$
$θ = {11.54}^{\circ} + 180^{\circ}$ $theta=11.54^@+180^@$
$θ \approx {191.54}^{\circ}$ $theta~~191.54^@$

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How do you calculate ${csc}^{- 1} (- 5)$ $csc^-1(-5)$ ?

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Explanation:

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