Incorrect. For an angle $\displaystyle\theta\usepackage{cmbright}\Huge\$ in standard position, with the terminal side intersecting the unit circle at the point $\displaystyle{\left({x},{y}\right)}\usepackage{cmbright}\Huge\$ , the following holds:

$\displaystyle{\sin{\theta}}={y},{\cos{\theta}}={x},{\tan{\theta}}=\frac{{y}}{{x}},{\csc{\theta}}=\frac{{1}}{{\sin{\theta}}}=\frac{{1}}{{y}},\usepackage{cmbright}\Huge\$

$\displaystyle{\sec{\theta}}=\frac{{1}}{{\cos{\theta}}}=\frac{{1}}{{x}},{\cot{\theta}}=\frac{{1}}{{\tan{\theta}}}=\frac{{x}}{{y}}\usepackage{cmbright}\Huge\$