Question

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

Answer 1

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

Explanation:

`csc (alpha/2) = 2.3`

`1 / sin (alpha / 2) = 2.3`

`sin (alpha / 2) = 1/ 2.3`

`alpha / 2 = sin ^ (-1) (1/2.3)`

`alpha / 2 = 25.77^@`

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