Chapter 3 - Radian Measure and the Unit Circle - Section 3.3 The Unit Circle and Circular Functions - 3.3 Exercises - Page 125: 83

Since $x$ is positive and $y$ is positive, an angle of 51 radians is in the first quadrant.

$\frac{x}{r} = cos~\theta$ $\frac{x}{r} = cos~(51~rad)$ $\frac{x}{r} = 0.74$ Since $r$ is always positive, $x$ is positive. $\frac{y}{r} = sin~\theta$ $\frac{y}{r} = sin~(51~rad)$ $\frac{y}{r} = 0.67$ Since $r$ is always positive, $y$ is positive. Since $x$ is positive and $y$ is positive, an angle of 51 radians is in the first quadrant.