Question

Arc AB is One-sixth of the circumference of a circle. What is the radian measure of the central angle? StartFraction pi over 6 EndFraction StartFraction pi Over 3 EndFraction StartFraction 2 pi Over 3 EndFraction StartFraction 5 pi Over 6 EndFraction

Answer 1

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:

$\text{Area of Sector} = \frac{\text{Central Angle}}{2 \pi} \times \text{Area of Circle}$

The length of arc:

$\text{Length of Arc} = \frac{\text{Central Angle}}{2 \pi} \times \text{Circumference of Circle}$

Let us now tackle the problem!

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This problem is about finding the central angle of circle.

$\text{Length of Arc} = \frac{\text{Central Angle}}{2 \pi} \times \text{Circumference of Circle}$

$\frac{1}{6} \times \text{Circumference of Circle} = \frac{\text{Central Angle}}{2 \pi} \times \text{Circumference of Circle}$

$\frac{1}{6} = \frac{\text{Central Angle}}{2 \pi}$

$\text{Central Angle} = \frac{1}{6} \times {2 \pi}$

$\text{Central Angle} = \frac{1}{3} \times {\pi}$

$\text{Central Angle} = \frac{1}{3}\pi \texttt{ radian}$

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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 : brainly.com/question/12438587
• Periodic Functions and Trigonometry : brainly.com/question/9718382
• Trigonometry Formula : 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

Answer 2

Answer:

StartFraction pi Over 3 EndFraction

Step-by-step explanation:

we know that

The circumference of a circle subtends a central angle of 360 degrees or 2π radians

so

by proportion

Find out the central angle for an arc equal to One-sixth of the circumference of a circle

Let

x -----> the measure of the central angle in radians for an arc equal to One-sixth of the circumference

$\frac{C}{2\pi}=\frac{(C/6)}{x}\\\\x=2\pi(C/6)/C\\\\x=\frac{2\pi}{6}$

Simplify

$x=\frac{\pi}{3}$

therefore

StartFraction pi Over 3 EndFraction