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White raven [17]
3 years ago
8

Please help with these two questions I'm very confused!

Mathematics
1 answer:
Lerok [7]3 years ago
6 0
1)

\bf \textit{Cofunction Identities}
\\\\
sin\left(\frac{\pi}{2}-\theta\right)=cos(\theta)
\qquad 
cos\left(\frac{\pi}{2}-\theta\right)=sin(\theta)
\\\\\\
\textit{also recall that }sin(-\theta )=-sin(\theta )\\\\
-------------------------------

\bf sin\left( \theta -\frac{\pi }{2} \right)\implies sin\left[-\left( \frac{\pi }{2}-\theta \right)  \right]\implies -sin\left( \theta -\frac{\pi }{2} \right)\implies -cos(\theta )
\\\\\\
\textit{and since }cos(\theta )=0.54\qquad then\qquad -cos(\theta )\implies -0.54



2)

\bf \textit{Cofunction Identities}
\\\\
sin\left(\frac{\pi}{2}-\theta\right)=cos(\theta)
\qquad 
cos\left(\frac{\pi}{2}-\theta\right)=sin(\theta)
\\\\\\
tan\left(\frac{\pi}{2}-\theta\right)=cot(\theta)\qquad 
cot\left(\frac{\pi}{2}-\theta\right)=tan(\theta)
\\\\\\
\textit{also recall }sin(-\theta )=-sin(\theta )\qquad cos(-\theta )=cos(\theta )\\\\
-------------------------------

\bf tan\left( x-\frac{\pi }{2} \right)\implies \cfrac{sin\left( x-\frac{\pi }{2} \right)}{cos\left( x-\frac{\pi }{2} \right)}\implies \cfrac{sin\left[ -\left( \frac{\pi }{2}-x \right) \right]}{cos\left[ -\left( \frac{\pi }{2}-x \right) \right]}
\\\\\\
\cfrac{-sin\left( \frac{\pi }{2}-x \right)}{cos\left( \frac{\pi }{2}-x \right)}\implies -tan\left( \frac{\pi }{2}-x \right)\implies -cot(x)
\\\\\\
\textit{and since }cot(x)=-0.18\qquad then\qquad -cot(x)\implies 0.18
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