Chapter 4.1, Problem 41E

(a)

To determine

Sketch the angle ${405}^0$ in standard Position.

Explanation of Solution

Given:

The angle ${405}^0$

Concept Used:

An angle is in "standard position" when the vertex is at the origin and the initial side of the angle is along the positive x-axis.

Calculation:

  

A Positive angle measured in counter clockwise direction from the Horizontal (x-axis).

Thus, the initial side of the angle ${405}^0$ is coincides with Positive side Horizontal Axis and the Terminal Side of the angle half way from Horizontal axis and the positive side of the vertical axis with a full round into counter clock wise direction.

(b)

To determine

Sketch the angle $-{780}^0$ in standard Position.

Explanation of Solution

Given:

The angle $-{780}^0$

Concept Used:

An angle is in "standard position" when the vertex is at the origin and the initial side of the angle is along the positive x-axis.

Calculation:

  

Calculation:

A Negative angle measured in clockwise direction from the Horizontal axis .

Thus, the initial side of the angle $-{780}^0$ is coincides with Positive side Horizontal Axis and the Terminal Side of the angle lies two − third way between the negative side of Horizontal axis and the Negative side of the Vertical axis with two full rotation in clockwise direction.