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

Quadrant III

1.$\cos\theta=\frac{x}{r}$ If cosine is negative, that means x must be negative (since r is always negative) That can be only II and III quadrants 2.$\sin\theta=\frac{y}{r}$ If sine is negative, that means y must be negative (since r is always negative) That can be only II and IV quadrants 3. For both sine and cosine to be negative, we must be in Quadrant III