Chapter 3 - Radian Measure and the Unit Circle - Section 3.3 The Unit Circle and Circular Functions - 3.3 Exercises - Page 125: 85

Since $x$ is negative and $y$ is positive, an angle of 65 radians is in the second quadrant.

$\frac{x}{r} = cos~\theta$ $\frac{x}{r} = cos~(65~rad)$ $\frac{x}{r} = -0.56$ Since $r$ is always positive, $x$ is negative. $\frac{y}{r} = sin~\theta$ $\frac{y}{r} = sin~(65~rad)$ $\frac{y}{r} = 0.83$ Since $r$ is always positive, $y$ is positive. Since $x$ is negative and $y$ is positive, an angle of 65 radians is in the second quadrant.