Respuesta :
[tex]\bf 3sin^2(\theta )+16sin(\theta )-35=0\impliedby
\begin{array}{llll}
\textit{notice this is just a quadratic }\\\\ax^2+bx+c=0
\end{array}
\\\\\\\
[3sin(\theta )-5][sin(\theta )+7]=0\\\\
-------------------------------\\\\
3sin(\theta )-5=0\implies 3sin(\theta )=5\implies sin(\theta )=\cfrac{5}{3}
\\\\\\
\measuredangle \theta =sin^{-1}\left( \frac{5}{3} \right)[/tex]
now, before continuing on the first root, recall that the sine has a range of -1 ⩽ sin(θ) ⩽1, however 5/3 is greater than 1, and therefore is out of range, meaning, there's no such angle, so we've got zilch there.
now, let's check the second root,
[tex]\bf sin(\theta )+7=0\implies sin(\theta )=-7\implies \measuredangle \theta =sin^{-1}(-7)[/tex]
well, hell -7 is smaller than -1, so is also outside the range for sine, and so, the second root gave also zilch, so, in short, there's no such angle.
now, before continuing on the first root, recall that the sine has a range of -1 ⩽ sin(θ) ⩽1, however 5/3 is greater than 1, and therefore is out of range, meaning, there's no such angle, so we've got zilch there.
now, let's check the second root,
[tex]\bf sin(\theta )+7=0\implies sin(\theta )=-7\implies \measuredangle \theta =sin^{-1}(-7)[/tex]
well, hell -7 is smaller than -1, so is also outside the range for sine, and so, the second root gave also zilch, so, in short, there's no such angle.
