# How do you evaluate csc^-1 (-7/3)?

##### 1 Answer
Jun 5, 2016

$\theta = - 25.3769 \text{ to 4 decimal places}$ (clockwise -> 4rd quadrant)

#### Explanation:

$\text{cosec"(theta)" is } \frac{1}{\sin} \left(\theta\right)$

=>"cosec"(theta)" is "1/[("opposite")/("hypotenuse")] =("hypotenuse")/("opposite")-> -7/3

I have made $y$ negative so that we have $= - \frac{7}{3}$

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From the diagram $\sin \left(\theta\right) = - \frac{3}{7}$

So ${\sin}^{1} \left(- \frac{3}{7}\right) = \theta = - 25.3769$ to 4 decimal places