Chapter 1 - Trigonometric Functions - Section 1.4 Using the Definitions of the Trigonometric Functions - 1.4 Exercises - Page 36: 37

Quadrant I

1.$\sec\theta=\frac{r}{x}$ If secant is positive, that means x must be positive (since r is always positive) That can be only I and IV quadrants 2.$\csc\theta=\frac{r}{y}$ If cosecant is positive, that means y must be positive (since r is always poitive) That can be only I and II quadrants 3. For both secant and cosecant to be positive, we must be in Quadrant I