If cosine theta equals one over six, what are the values of sin θ and tan θ? A) sine theta equals plus or minus seven times square root of five over six, tangent theta equals plus or minus seven times square root of five B) sine theta equals plus or minus square root of thirty-five over six, tangent theta equals negative seven times square root of five C) sine theta equals plus or minus seven times square root of five over six, tangent theta equals negative square root of thirty five D) sine theta equals plus or minus square root of thirty-five over six, tangent theta equals plus or minus square root of thirty five

Answer:Option D.  sine theta equals plus or minus square root of thirty-five over six, tangent theta equals plus or minus square root of thirty fiveStep-by-step explanation:we have that[tex]cos(\theta)=\frac{1}{6}[/tex]If the cosine is positive, then the angle theta lie on the first or fourth QuadrantthereforeThe sine of angle theta could be positive (I Quadrant) or negative (IV Quadrant) and the tangent of angle theta could be positive (I Quadrant) or negative (IV Quadrant)step 1Find [tex]sin(\theta)[/tex]Remember that[tex]sin^{2} (\theta)+cos^{2} (\theta)=1[/tex]we have[tex]cos(\theta)=\frac{1}{6}[/tex]substitute[tex]sin^{2} (\theta)+(\frac{1}{6})^{2}=1[/tex][tex]sin^{2} (\theta)+\frac{1}{36}=1[/tex][tex]sin^{2} (\theta)=1-\frac{1}{36}[/tex][tex]sin^{2} (\theta)=\frac{35}{36}[/tex][tex]sin(\theta)=(+/-)\frac{\sqrt{35}}{6}[/tex]sosine theta equals plus or minus square root of thirty-five over sixstep 2Find [tex]tan(\theta)[/tex]Remember that[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]we have[tex]sin(\theta)=(+/-)\frac{\sqrt{35}}{6}[/tex][tex]cos(\theta)=\frac{1}{6}[/tex]substitute[tex]tan(\theta)=(+/-)\sqrt{35}[/tex]tangent theta equals plus or minus square root of thirty five