Respuesta :
first at all, we are gonna solve this using inverse trigonometric functions
like this:
[tex]\begin{gathered} \sin \alpha\text{ = x} \\ \alpha\text{ = }\sin ^{-1}x \end{gathered}[/tex]for the first case:
a)
[tex]\begin{gathered} \sin \alpha\text{ = }0.3697 \\ \alpha=\sin ^{-1}(0.3697) \\ \alpha=21.697\ldots \\ \alpha\cong20 \end{gathered}[/tex]b)
[tex]\begin{gathered} \cos \alpha\text{ = }0.7265 \\ \alpha=\cos ^{-1}(0.7265) \\ \alpha=43.406\ldots \\ \alpha\cong40 \end{gathered}[/tex]c)
In this case, we are going to use the following trigonometric identity:
[tex]\begin{gathered} \sec \alpha=\frac{1}{\cos \alpha} \\ \end{gathered}[/tex]later,
[tex]\begin{gathered} \sec \alpha=2.3232 \\ \frac{1}{\cos \alpha}=2.3232 \\ \cos \alpha=\frac{1}{2.3232} \\ \alpha=\cos ^{-1}(\frac{1}{2.3232}) \\ \alpha=64.504\ldots \\ \alpha\cong60 \end{gathered}[/tex]d)
In this case, we are going to use the following trigonometric identity:
[tex]\begin{gathered} csc\alpha=\frac{1}{sin\alpha} \\ \end{gathered}[/tex]later,
[tex]\begin{gathered} \csc \alpha=1.1234 \\ \frac{1}{sin\alpha}=1.1234 \\ \sin \alpha=\frac{1}{1.1234} \\ \alpha=\sin ^{-1}(\frac{1}{1.1234}) \\ \alpha=62.892\ldots \\ \alpha\cong60 \end{gathered}[/tex]finally, those are your answers.
