How do you solve: sin(x) = -0.78 on 0 ≤ x ≤ 2π ?

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Additional info given: There are two solutions, A and B, with A < B.

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Answer 1 · 2016-07-22T06:04:42

$x = {231.78}^{o}$ $x=231.78^o$ and $x = {308.22}^{o}$ $x=308.22^o$

Within the range $0 \leq x \leq 2 π$ $0<=x<=2pi$ , $sin x$ $sinx$ is negative in third and fourth quadrant.

As $sin x = - 0.78$ $sinx=-0.78$ (as ${sin 51.78}^{o} = 0.78$ $sin51.78^o=0.78$ )

$x = {(180 + 51.78)}^{o} = {231.78}^{o}$ $x=(180+51.78)^o=231.78^o$ and

$x = {(360 - 51.78)}^{o} = {308.22}^{o}$ $x=(360-51.78)^o=308.22^o$