4. The angle 0 = 48° intersects the Unit Circle at the point (0.669, 0.743). Using what you know about 0 = 48°, determine the coordinates of the angle 228°. Explain how you got your answer. 90 48° (0.669, 0.743) 180 0° 360° 270 "hint" where would 228° be on the unit circle and how does it relate to 48°7
4. The angle 0 = 48° intersects the Unit Circle at the point (0.669, 0.743). Using what you know about 0 = 48°, determine the coordinates of the angle 228°. Explain how you got your answer. 90 48° (0.669, 0.743) 180 0° 360° 270 "hint" where would 228° be on the unit circle and how does it relate to 48°7
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter2: Right Triangle Trigonometry
Section2.4: Applications
Problem 48PS: Albert lives in New Orleans. At noon on a summer day, the angle of elevation of the sun is 84. The...
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![**Question:**
The angle θ = 48° intersects the Unit Circle at the point (0.669, 0.743). Using what you know about θ = 48°, determine the coordinates of the angle 228°. Explain how you got your answer.
**Hint:** Where would 228° be on the unit circle and how does it relate to 48°?
**Answer Explanation:**
1. **Identify the Reference Angle:**
- The angle 228° can be broken down to find its reference angle by subtracting it from 180°:
\( \text{Reference Angle} = 228° - 180° = 48° \).
2. **Locate the Quadrant:**
- An angle of 228° lies in the third quadrant of the Unit Circle.
3. **Understand Coordinate Signs in Quadrants:**
- In the third quadrant, both sine and cosine are negative.
4. **Apply Reference Angle Coordinates:**
- Given that the coordinates for the reference angle of 48° are (0.669, 0.743), the coordinates of 228° will have the same absolute values but both will be negative due to the third quadrant's sign convention.
5. **Determine the Coordinates:**
- Therefore, the coordinates for 228° are: (-0.669, -0.743).
**Graph Description:**
The graph shown is the unit circle with angles marked at the four quadrants: 0°/360° (right), 90° (top), 180° (left), and 270° (bottom). There is a line at an angle of 48° from the positive x-axis, intersecting the unit circle, with the point noted as (0.669, 0.743).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86d17ae2-ae86-4edb-8c64-c8a7246a4613%2Ff89f1451-a4b2-4b54-8328-0b5c592b18b9%2Fsmro9q7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
The angle θ = 48° intersects the Unit Circle at the point (0.669, 0.743). Using what you know about θ = 48°, determine the coordinates of the angle 228°. Explain how you got your answer.
**Hint:** Where would 228° be on the unit circle and how does it relate to 48°?
**Answer Explanation:**
1. **Identify the Reference Angle:**
- The angle 228° can be broken down to find its reference angle by subtracting it from 180°:
\( \text{Reference Angle} = 228° - 180° = 48° \).
2. **Locate the Quadrant:**
- An angle of 228° lies in the third quadrant of the Unit Circle.
3. **Understand Coordinate Signs in Quadrants:**
- In the third quadrant, both sine and cosine are negative.
4. **Apply Reference Angle Coordinates:**
- Given that the coordinates for the reference angle of 48° are (0.669, 0.743), the coordinates of 228° will have the same absolute values but both will be negative due to the third quadrant's sign convention.
5. **Determine the Coordinates:**
- Therefore, the coordinates for 228° are: (-0.669, -0.743).
**Graph Description:**
The graph shown is the unit circle with angles marked at the four quadrants: 0°/360° (right), 90° (top), 180° (left), and 270° (bottom). There is a line at an angle of 48° from the positive x-axis, intersecting the unit circle, with the point noted as (0.669, 0.743).
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