Question

sketch θ = -\frac{π}{3} in standard position.

Explanation:

Step1: Recall standard - position of an angle

In standard position, an angle $\theta$ has its vertex at the origin $(0,0)$ of the coordinate - plane and its initial side along the positive $x$ - axis. A negative angle is measured clockwise.

Step2: Determine the position of $\theta =-\frac{\pi}{3}$

Since $\theta =-\frac{\pi}{3}= - 60^{\circ}$ (because $\pi$ radians $ = 180^{\circ}$), we start from the positive $x$ - axis and rotate clockwise by $60^{\circ}$. The terminal side of the angle $\theta =-\frac{\pi}{3}$ will be in the fourth quadrant, making an angle of $60^{\circ}$ with the positive $x$ - axis in the clockwise direction.

Answer:

To sketch $\theta =-\frac{\pi}{3}$ in standard position:

1. Draw the $x$ and $y$ axes intersecting at the origin $(0,0)$.
2. Mark the positive $x$ - axis as the initial side of the angle.
3. Rotate the terminal side of the angle clockwise by $60^{\circ}$ (or $\frac{\pi}{3}$ radians) from the positive $x$ - axis. The terminal side will lie in the fourth quadrant.