Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To determine the angle of rotation that maps the point [tex]\((0, -2)\)[/tex] to [tex]\((2, 0)\)[/tex], we can follow these steps:
1. Identify the coordinates:
- The initial point is [tex]\((0, -2)\)[/tex].
- The final point is [tex]\((2, 0)\)[/tex].
2. Determine the initial angle:
- The initial angle [tex]\(\theta_1\)[/tex] is the angle between the positive x-axis and the line connecting the origin to the point [tex]\((0, -2)\)[/tex].
- Since [tex]\((0, -2)\)[/tex] lies directly below the origin on the y-axis, the angle [tex]\(\theta_1\)[/tex] is -90 degrees (or alternatively [tex]\(-\frac{\pi}{2}\)[/tex] radians).
3. Determine the final angle:
- The final angle [tex]\(\theta_2\)[/tex] is the angle between the positive x-axis and the line connecting the origin to the point [tex]\((2, 0)\)[/tex].
- Since [tex]\((2, 0)\)[/tex] lies directly on the positive x-axis from the origin, the angle [tex]\(\theta_2\)[/tex] is 0 degrees (or 0 radians).
4. Calculate the angle of rotation:
- The angle of rotation is the difference between the final angle [tex]\(\theta_2\)[/tex] and the initial angle [tex]\(\theta_1\)[/tex].
- [tex]\(\theta_{\text{rotation}} = \theta_2 - \theta_1\)[/tex].
5. Convert angles to radians (if necessary):
- Initial angle: [tex]\(\theta_1 = -\frac{\pi}{2}\)[/tex] radians.
- Final angle: [tex]\(\theta_2 = 0\)[/tex] radians.
6. Compute the rotation in radians:
- [tex]\(\theta_{\text{rotation}} = 0 - (-\frac{\pi}{2}) = \frac{\pi}{2}\)[/tex] radians.
7. Convert the rotation angle from radians to degrees:
- To convert radians to degrees, we use the conversion factor [tex]\(180^\circ / \pi\)[/tex].
- [tex]\(\frac{\pi}{2} \times \frac{180^\circ}{\pi} = 90^\circ\)[/tex].
Therefore, the angle measure of the rotation that maps the point [tex]\((0, -2)\)[/tex] to [tex]\((2, 0)\)[/tex] is [tex]\(90\)[/tex] degrees.
1. Identify the coordinates:
- The initial point is [tex]\((0, -2)\)[/tex].
- The final point is [tex]\((2, 0)\)[/tex].
2. Determine the initial angle:
- The initial angle [tex]\(\theta_1\)[/tex] is the angle between the positive x-axis and the line connecting the origin to the point [tex]\((0, -2)\)[/tex].
- Since [tex]\((0, -2)\)[/tex] lies directly below the origin on the y-axis, the angle [tex]\(\theta_1\)[/tex] is -90 degrees (or alternatively [tex]\(-\frac{\pi}{2}\)[/tex] radians).
3. Determine the final angle:
- The final angle [tex]\(\theta_2\)[/tex] is the angle between the positive x-axis and the line connecting the origin to the point [tex]\((2, 0)\)[/tex].
- Since [tex]\((2, 0)\)[/tex] lies directly on the positive x-axis from the origin, the angle [tex]\(\theta_2\)[/tex] is 0 degrees (or 0 radians).
4. Calculate the angle of rotation:
- The angle of rotation is the difference between the final angle [tex]\(\theta_2\)[/tex] and the initial angle [tex]\(\theta_1\)[/tex].
- [tex]\(\theta_{\text{rotation}} = \theta_2 - \theta_1\)[/tex].
5. Convert angles to radians (if necessary):
- Initial angle: [tex]\(\theta_1 = -\frac{\pi}{2}\)[/tex] radians.
- Final angle: [tex]\(\theta_2 = 0\)[/tex] radians.
6. Compute the rotation in radians:
- [tex]\(\theta_{\text{rotation}} = 0 - (-\frac{\pi}{2}) = \frac{\pi}{2}\)[/tex] radians.
7. Convert the rotation angle from radians to degrees:
- To convert radians to degrees, we use the conversion factor [tex]\(180^\circ / \pi\)[/tex].
- [tex]\(\frac{\pi}{2} \times \frac{180^\circ}{\pi} = 90^\circ\)[/tex].
Therefore, the angle measure of the rotation that maps the point [tex]\((0, -2)\)[/tex] to [tex]\((2, 0)\)[/tex] is [tex]\(90\)[/tex] degrees.
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
