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

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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

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Answer 1 · 2018-06-18T09:53:56

$α = {51.5}^{\circ}, rounded to the nearest tenth of a degree$ $color(crimson)(alpha = 51.5^@, " rounded to the nearest tenth of a degree"$

Explanation:

$csc (\frac{α}{2}) = 2.3$ $csc (alpha/2) = 2.3$

$\frac{1}{sin (\frac{α}{2})} = 2.3$ $1 / sin (alpha / 2) = 2.3$

$sin (\frac{α}{2}) = \frac{1}{2.3}$ $sin (alpha / 2) = 1/ 2.3$

$\frac{α}{2} = {sin}^{- 1} (\frac{1}{2.3})$ $alpha / 2 = sin ^ (-1) (1/2.3)$

$\frac{α}{2} = {25.77}^{\circ}$ $alpha / 2 = 25.77^@$

$α = 2 \cdot 25.77 = 51.54 = {51.5}^{\circ}, rounded to the nearest tenth of a degree$ $color(crimson)(alpha = 2 * 25.77 = 51.54 = 51.5^@, " rounded to the nearest tenth of a degree"$

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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

1 Answer

Explanation:

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