which of the following is true of the location of an angle, $\theta$, whose tangent value is…

which of the following is true of the location of an angle, $\theta$, whose tangent value is $-\frac{sqrt{3}}{3}$?\n$\theta$ has a 30 - degree reference angle and is located in quadrant ii or iv\n$\theta$ has a 30 - degree reference angle and is located in quadrant ii or iii\n$\theta$ has a 60 - degree reference angle and is located in quadrant ii or iv\n$\theta$ has a 60 - degree reference angle and is located in quadrant ii or iii

which of the following is true of the location of an angle, $\theta$, whose tangent value is $-\frac{sqrt{3}}{3}$?\n$\theta$ has a 30 - degree reference angle and is located in quadrant ii or iv\n$\theta$ has a 30 - degree reference angle and is located in quadrant ii or iii\n$\theta$ has a 60 - degree reference angle and is located in quadrant ii or iv\n$\theta$ has a 60 - degree reference angle and is located in quadrant ii or iii

Answer

Answer:

A. $\theta$ has a 30 - degree reference angle and is located in Quadrant II or IV

Explanation:

Step1: Recall tangent values

We know that $\tan30^{\circ}=\frac{\sqrt{3}}{3}$ and $\tan\theta =-\frac{\sqrt{3}}{3}$. The negative sign of the tangent value indicates that the angle $\theta$ is in either Quadrant II or IV (since $\tan\theta=\frac{y}{x}$ and it is negative when $x$ and $y$ have opposite signs).

Step2: Determine reference angle

The reference - angle is the acute angle between the terminal side of the angle and the $x$ - axis. Since the absolute value of $\tan\theta$ is $\frac{\sqrt{3}}{3}$, the reference angle is $30^{\circ}$ (because $\tan30^{\circ}=\frac{\sqrt{3}}{3}$). So the angle $\theta$ has a 30 - degree reference angle and is located in Quadrant II or IV.