Incorrect. Since $\displaystyle{\sin{\theta}}={y}\usepackage{cmbright}\Huge\$ , sine is positive when $\displaystyle{y}>{0}\usepackage{cmbright}\Huge\$ .This occurs in Quadrants I and II.

Since $\displaystyle{\cos{\theta}}={x}\usepackage{cmbright}\Huge\$ , cosine is positive when $\displaystyle{x}>{0}\usepackage{cmbright}\Huge\$ . This occurs in Quadrants I and IV.

Since $\displaystyle{\tan{\theta}}=\frac{{y}}{{x}}\usepackage{cmbright}\Huge\$ , tangent is positive when x and y are both positive or both negative. This occurs in Quadrants I and III.

Since secant is the reciprocal of cosine, they have the same sign. Similarly, cosecant and sine have the same sign; tangent and cotangent have the same sign.