How do you find the value for ${csc}^{- 1} (- \frac{7}{3})$ $csc^-1 (-7/3)$ ?

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How do you find the value for ${csc}^{- 1} (- \frac{7}{3})$ $csc^-1 (-7/3)$ ?

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Answer 1 · 2018-05-22T00:02:05

csc x = (-7/3). Find arc x
sin x = - 3/7
Calculator and unit circle give 2 solutions for x -->
$x = - 25^{\circ} 38 + k 360^{\circ}$ $x = - 25^@38 + k360^@$ , and
$x = 180 - (- 25.38) = 180 + 25.38 = 205^{\circ} 38 + k 360^{\circ}$ $x = 180 - (- 25.38) = 180 + 25.38 = 205^@38 + k360^@$
Note. x = -25.38 is co-terminal to x = 360 - 25.38 = 334.62
Answers:
$x = 205^{\circ} 38 + k 360^{\circ}$ $x = 205^@38 + k360^@$
$x = 334^{\circ} 62 + k 360^{\circ}$ $x = 334^@62 + k360^@$

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How do you find the value for ${csc}^{- 1} (- \frac{7}{3})$ $csc^-1 (-7/3)$ ?

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