Cotangent and tangent are reciprocals, as they should be. However, you cannot have this value of cosine for the same angle. Since $\displaystyle{\tan{{X}}}=\frac{{2}}{{3}}\usepackage{cmbright}\Huge\$ , you could have $\displaystyle{o}={2}\usepackage{cmbright}\Huge\$ and $\displaystyle{a}={3}\usepackage{cmbright}\Huge\$ . If $\displaystyle{\cos{{X}}}=\frac{{3}}{{4}}=\frac{{a}}{{h}}\usepackage{cmbright}\Huge\$ , then $\displaystyle{h}={4}\usepackage{cmbright}\Huge\$ . But the lengths 2, 3, and 4 do not satisfy the Pythagorean Theorem. The correct answer is: $\displaystyle{\sin{{X}}}=\frac{{3}}{{4}}\usepackage{cmbright}\Huge\$ , $\displaystyle{\cot{{X}}}=\frac{\sqrt{{7}}}{{3}}\usepackage{cmbright}\Huge\$ , $\displaystyle{\tan{{X}}}=\frac{{3}}{\sqrt{{7}}}\usepackage{cmbright}\Huge\$