Determine the quadrant that an angle measuring 1,282 degrees is in if the angle is drawn in standard position.
Determine the quadrant that an angle measuring 1,282 degrees is in if the angle is drawn in standard position.
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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![**Determine the Quadrant of an Angle Measuring 1,282 Degrees**
When an angle is drawn in standard position (with its initial side along the positive x-axis), we can determine its quadrant by finding its equivalent angle between 0 and 360 degrees. Here’s a step-by-step method to find the quadrant for an angle of 1,282 degrees:
1. **Find the Coterminal Angle:**
- To get an equivalent angle between 0 and 360 degrees, subtract 360 degrees from 1,282 degrees repeatedly until the result is between 0 and 360 degrees.
- For 1,282 degrees:
\[
1,282 - 360 = 922 \text{ degrees}
\]
\[
922 - 360 = 562 \text{ degrees}
\]
\[
562 - 360 = 202 \text{ degrees}
\]
2. **Determine the Quadrant:**
- Now, we have an angle of 202 degrees. To determine the quadrant, note the following ranges:
- Quadrant I: 0 to 90 degrees
- Quadrant II: 90 to 180 degrees
- Quadrant III: 180 to 270 degrees
- Quadrant IV: 270 to 360 degrees
- Since 202 degrees lies between 180 degrees and 270 degrees, the angle is in **Quadrant III**.
So, an angle measuring 1,282 degrees is in **Quadrant III** when drawn in standard position.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd24861ef-92b0-4cd8-8c54-2ac2200498ec%2F8d849a98-016c-490f-bad8-666fbc7bc18d%2Fsrbtfj7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determine the Quadrant of an Angle Measuring 1,282 Degrees**
When an angle is drawn in standard position (with its initial side along the positive x-axis), we can determine its quadrant by finding its equivalent angle between 0 and 360 degrees. Here’s a step-by-step method to find the quadrant for an angle of 1,282 degrees:
1. **Find the Coterminal Angle:**
- To get an equivalent angle between 0 and 360 degrees, subtract 360 degrees from 1,282 degrees repeatedly until the result is between 0 and 360 degrees.
- For 1,282 degrees:
\[
1,282 - 360 = 922 \text{ degrees}
\]
\[
922 - 360 = 562 \text{ degrees}
\]
\[
562 - 360 = 202 \text{ degrees}
\]
2. **Determine the Quadrant:**
- Now, we have an angle of 202 degrees. To determine the quadrant, note the following ranges:
- Quadrant I: 0 to 90 degrees
- Quadrant II: 90 to 180 degrees
- Quadrant III: 180 to 270 degrees
- Quadrant IV: 270 to 360 degrees
- Since 202 degrees lies between 180 degrees and 270 degrees, the angle is in **Quadrant III**.
So, an angle measuring 1,282 degrees is in **Quadrant III** when drawn in standard position.
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