Question

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

1) If cos θ = 0.54, find sin(θ-pi/2).
2) If cot x = -0.18, find tan(x-pi/2).

Answer 1

1)


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


`\bf sin\left( \theta -(\pi )/(2) \right)\implies sin\left[-\left( (\pi )/(2)-\theta \right) \right]\implies -sin\left( \theta -(\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((\pi)/(2)-\theta\right)=cos(\theta) \qquad cos\left((\pi)/(2)-\theta\right)=sin(\theta) \\\\\\ tan\left((\pi)/(2)-\theta\right)=cot(\theta)\qquad cot\left((\pi)/(2)-\theta\right)=tan(\theta) \\\\\\ \textit{also recall }sin(-\theta )=-sin(\theta )\qquad cos(-\theta )=cos(\theta )\\\\ -------------------------------`


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