The radian measure of the central angle is π/3 radian
Further explanation
The basic formula that need to be recalled is:
Circular Area = π x R²
Circle Circumference = 2 x π x R
where:
R = radius of circle
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The area of sector:
[tex]\text{Area of Sector} = \frac{\text{Central Angle}}{2 \pi} \times \text{Area of Circle}[/tex]
The length of arc:
[tex]\text{Length of Arc} = \frac{\text{Central Angle}}{2 \pi} \times \text{Circumference of Circle}[/tex]
Let us now tackle the problem!
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This problem is about finding the central angle of circle.
[tex]\text{Length of Arc} = \frac{\text{Central Angle}}{2 \pi} \times \text{Circumference of Circle}[/tex]
[tex]\frac{1}{6} \times \text{Circumference of Circle} = \frac{\text{Central Angle}}{2 \pi} \times \text{Circumference of Circle}[/tex]
[tex]\frac{1}{6} = \frac{\text{Central Angle}}{2 \pi}[/tex]
[tex]\text{Central Angle} = \frac{1}{6} \times {2 \pi}[/tex]
[tex]\text{Central Angle} = \frac{1}{3} \times {\pi}[/tex]
[tex]\text{Central Angle} = \frac{1}{3}\pi \texttt{ radian}[/tex]
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Conclusion:
The radian measure of the central angle is π/3 radian
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Learn more
- Calculate Angle in Triangle : https://brainly.com/question/12438587
- Periodic Functions and Trigonometry : https://brainly.com/question/9718382
- Trigonometry Formula : https://brainly.com/question/12668178
Answer details
Grade: College
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse, Circle , Arc , Sector , Area, Central Angle , Angle
