#### Answer

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

#### Work Step by Step

$\frac{x}{r} = cos~\theta$
$\frac{x}{r} = cos~(51~rad)$
$\frac{x}{r} = 0.74$
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.