Chapter 4.1, Problem 23E

(a)

To determine

Sketch the angle $\text{5π}$ in standard Position.

Explanation of Solution

Given:

The angle $\text{5π}$

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 $\text{5π}$ is coincides with Positive side Horizontal Axis and the Terminal Side of the angle coincide with the positive side of Vertical axis.

(b)

To determine

Sketch the angle − 4in standard Position.

Explanation of Solution

Given:

The angle− 4

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:

We know that 1 radian = 57.29 deg

Now we can write

− 4 radian = − 4 5(57.29) = − 219.16 deg

  $-{180}^0<-{219.16}^0<-{270}^0$ ; Angle − 4 radians lie in the second Quadrant.

A Negative angle measured in clockwise direction from the Horizontal

Thus, the initial side of the angle − 4 radians is coincides with Positive side Horizontal Axis and the Terminal Side of the angle is in the half way of second quadrant.