Problem 46 - Precalculus: A Concise Course

Question

Sketch each angle in standard position. (a) \(90^{\circ}\) (b) \(180^{\circ}\)

Step-by-Step Solution

Answer

The angle \(90^{\circ}\) in standard position has its terminal side along the positive y-axis, while the angle \(180^{\circ}\) in standard position has its terminal side along the negative x-axis.

Step 1: Understanding standard position

An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis. The initial side of the angle is the ray on the positive x-axis, the other ray represents the terminal side.

Step 2: Sketch angle \(90^{\circ}\)

The angle \(90^{\circ}\) in standard position starts with its initial side on the positive x-axis and rotates counterclockwise until it is vertical, pointing upwards on the positive y-axis. This indicates a \(90^{\circ}\) rotation from the x-axis.

Step 3: Sketch angle \(180^{\circ}\)

The angle \(180^{\circ}\) in standard position starts with its initial side on the positive x-axis and rotates counterclockwise until it is horizontal again, but pointing left on the negative x-axis. This indicates a \(180^{\circ}\) rotation from the x-axis.