# Find all values of α in degrees to satisfy this equation, round to approximate to the nearest tenth of a degree? csc(α/2)=-2.3

Jun 18, 2018

color(crimson)(alpha = 51.5^@, " rounded to the nearest tenth of a degree"

#### Explanation:

$\csc \left(\frac{\alpha}{2}\right) = 2.3$

$\frac{1}{\sin} \left(\frac{\alpha}{2}\right) = 2.3$

$\sin \left(\frac{\alpha}{2}\right) = \frac{1}{2.3}$

$\frac{\alpha}{2} = {\sin}^{- 1} \left(\frac{1}{2.3}\right)$

$\frac{\alpha}{2} = {25.77}^{\circ}$

color(crimson)(alpha = 2 * 25.77 = 51.54 = 51.5^@, " rounded to the nearest tenth of a degree"