Given sin theta= 6/11 and sec theta < 0, find cos theta and tan theta.

Answer: option a.Step-by-step explanation: By definition, we know that: [tex]cos^2(\theta)=1-sen^2(\theta)\\\\tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex] Substitute [tex]sin(\theta)=\frac{6}{11}[/tex] into the first equation, solve for the cosine and simplify. Then, you obtain: [tex]cos(\theta)=\±\sqrt{1-(\frac{6}{11})^2}\\\\cos(\theta)=\±\sqrt{\frac{85}{121}}\\\\ cos(\theta)=\±\frac{\sqrt{85}}{11}[/tex] As [tex]sec\theta<0[/tex] then [tex]cos\theta<0[/tex]: [tex]cos(\theta)=-\frac{\sqrt{85}}{11}[/tex] Now we can find [tex]tan\theta[/tex]: [tex]tan\theta=\frac{\frac{6}{11}}{-\frac{\sqrt{85}}{11}}\\\\tan\theta=-\frac{6\sqrt{85}}{85}[/tex]