Question

I can’t figure out #4 and #5 can you help? College calculus 1

Answer 1

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:

`\begin{gathered} \tan ^2(\alpha)+1=\sec (\alpha) \\ \tan ^2(\alpha)+1=(1)/(\cos (\alpha)) \\ (-3)^2+1=(1)/(\cos (\alpha)) \\ 9+1=(1)/(\cos(\alpha)) \\ 10\cos (\alpha)=1 \\ \cos (\alpha)=1-10 \\ \cos (\alpha)=-9 \end{gathered}`

As we know now the cosine of angle alpha, let's find the sine using an Identity:

`\begin{gathered} \tan (\alpha)=(\sin (\alpha))/(\cos (\alpha)) \\ -3=(\sin (\alpha))/(-9) \\ \sin (a)=27 \end{gathered}`