Question

given the angle $135^{\circ}$, find the following:

1. convert to radians.
2. positive coterminal angle.
3. sketch the angle $135^{\circ}$

Explanation:

Step1: Convert degrees to radians

Multiply by $\frac{\pi}{180^\circ}$:
$135^\circ \times \frac{\pi}{180^\circ} = \frac{135\pi}{180} = \frac{3\pi}{4}$

Step2: Find positive coterminal angle

Add $360^\circ$ to the original angle:
$135^\circ + 360^\circ = 495^\circ$

Step3: Sketch the angle

Start at positive x-axis, rotate counterclockwise $135^\circ$ (lands in Quadrant II, halfway between $90^\circ$ and $180^\circ$).

Answer:

1. Radian measure: $\frac{3\pi}{4}$
2. Positive coterminal angle: $495^\circ$
3. Sketch: A counterclockwise rotation of $135^\circ$ from the positive x-axis, terminating in the second quadrant.