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)
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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).
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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