Question

sketch θ = \frac{5pi}{4} in standard position. drag to show the angle.

Explanation:

Step1: Recall standard - position angle rules

An angle $\theta$ in standard position has its vertex at the origin $(0,0)$ and its initial side along the positive $x$ - axis.

Step2: Analyze the given angle $\theta=\frac{5\pi}{4}$

We know that $\pi=\ 180^{\circ}$, so $\frac{5\pi}{4}=\frac{5\times180^{\circ}}{4}=225^{\circ}$.

Step3: Determine the terminal - side location

Since $180^{\circ}<225^{\circ}<270^{\circ}$, the terminal side of the angle $\frac{5\pi}{4}$ lies in the third quadrant. To sketch it, start with the initial side on the positive $x$ - axis and rotate counter - clockwise by $225^{\circ}$.

Answer:

To sketch $\theta = \frac{5\pi}{4}$ in standard position, place the vertex at the origin, the initial side on the positive $x$ - axis, and rotate counter - clockwise by $225^{\circ}$ so that the terminal side lies in the third quadrant.