Sure, let's work through this step-by-step to determine the new direction after making [tex]\(\frac{1}{2}\)[/tex] of a revolution clockwise while initially facing east.
1. Initial Direction:
- You are initially facing east. In terms of compass directions and degrees, facing east corresponds to [tex]\(0^\circ\)[/tex].
2. Understanding Half a Revolution:
- A full revolution is [tex]\(360^\circ\)[/tex].
- So, [tex]\(\frac{1}{2}\)[/tex] of a revolution is half of [tex]\(360^\circ\)[/tex], which is:
[tex]\[
\frac{360^\circ}{2} = 180^\circ
\][/tex]
3. Clockwise Movement:
- Moving clockwise means you are turning to your right.
- Starting at [tex]\(0^\circ\)[/tex] (east) and moving [tex]\(180^\circ\)[/tex] clockwise means you add the [tex]\(180^\circ\)[/tex] to your starting angle.
4. Calculating the New Direction:
- Starting at [tex]\(0^\circ\)[/tex] and moving [tex]\(180^\circ\)[/tex] clockwise:
[tex]\[
0^\circ + 180^\circ = 180^\circ
\][/tex]
- [tex]\(180^\circ\)[/tex] corresponds to facing west.
So, the step-by-step solution shows that if you are initially facing east and you make [tex]\(\frac{1}{2}\)[/tex] of a revolution clockwise, you will end up facing west.
To summarize:
- Initial Direction: East [tex]\((0^\circ)\)[/tex]
- Angle Turned: [tex]\(180^\circ\)[/tex] clockwise
- Final Direction: West [tex]\((180^\circ)\)[/tex]
Therefore, after making [tex]\(\frac{1}{2}\)[/tex] of a revolution clockwise from facing east, you will end up facing west.
