Question

draw the terminal side of an angle in standard position that measures $-135^{circ}$.
hint: first plot a point at the origin, then plot a second point anywhere on the terminal side.

Explanation:

Step1: Understand the direction of negative angles

Negative angles are measured clockwise from the positive x - axis.

Step2: Calculate the equivalent positive angle

Since \(360^{\circ}- 135^{\circ}=225^{\circ}\), an angle of \(-135^{\circ}\) is equivalent to an angle of \(225^{\circ}\) measured clockwise.

Step3: Determine the quadrant

\(180^{\circ}<225^{\circ}<270^{\circ}\), so the terminal side lies in the third quadrant.

Step4: Plot the terminal side

Starting from the positive x - axis, rotate \(135^{\circ}\) clockwise. A point on the terminal side can be \((-1,-1)\) (using the unit - circle concept, for an angle \(\theta = 225^{\circ}\) or \(- 135^{\circ}\), \(\cos\theta=-\frac{\sqrt{2}}{2}\approx - 0.7\), \(\sin\theta=-\frac{\sqrt{2}}{2}\approx - 0.7\), and we can scale it to \((-1,-1)\) for simplicity in the grid).

Answer:

Plot the terminal side by rotating \(135^{\circ}\) clockwise from the positive x - axis. A sample point on the terminal side (in the third quadrant) can be \((-1,-1)\) (you can use a straight - edge to draw a line from the origin \((0,0)\) through the point \((-1,-1)\)).