sin(a)=27
1) In this question, we have the value of the tangent (α) in Quadrant IV since -π/2 is in Quadrant IV if we go Clockwise.
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2) Now, as suggested, let's use the identity that has been provided:
[tex]\begin{gathered} \tan ^2(\alpha)+1=\sec (\alpha) \\ \tan ^2(\alpha)+1=\frac{1}{\cos (\alpha)} \\ (-3)^2+1=\frac{1}{\cos (\alpha)} \\ 9+1=\frac{1}{\cos(\alpha)} \\ 10\cos (\alpha)=1 \\ \cos (\alpha)=1-10 \\ \cos (\alpha)=-9 \end{gathered}[/tex]
As we know now the cosine of angle alpha, let's find the sine using an Identity:
[tex]\begin{gathered} \tan (\alpha)=\frac{\sin (\alpha)}{\cos (\alpha)} \\ -3=\frac{\sin (\alpha)}{-9} \\ \sin (a)=27 \end{gathered}[/tex]
