What is the distance traveled if a ladybug walks $$\frac{4}{5}$$ of a rotation on a circle with radius 10 cm?

The distance traveled is $$s = 10 \times \frac{4}{5} \times 2\text{π} = 16\text{π} \text{ cm}$$ .

What is the angle in radians for $$\frac{3}{4}$$ of a rotation?

The angle in radians is $$\frac{3}{4} \times 2\text{π} = 1.5\text{π} \text{ rad}$$ .

If a ladybug walks $$\frac{1}{8}$$ of a rotation on a circle with radius 1 cm, what is the distance traveled?

The distance traveled is $$s = 1 \times \frac{1}{8} \times 2\text{π} = \frac{\text{π}}{4} \text{ cm}$$ .

What is the angle in radians if a ladybug walks $$\frac{1}{8}$$ of a rotation?

The angle in radians is $$\frac{1}{8} \times 2\text{π} = \frac{\text{π}}{4} \text{ rad}$$ .

What is the angle in radians for $$\frac{4}{5}$$ of a rotation?

The angle in radians is $$\frac{4}{5} \times 2\text{π} = 1.6\text{π} \text{ rad}$$ .

How do you find the distance traveled for a fraction of a rotation?

Multiply the fraction of the rotation by the circumference of the circle.

What is the formula for calculating the distance traveled along a circular path?

The formula is $$s = rθ$$ , where s is the distance, r is the radius, and θ is the angle in radians.

What is the circumference of a circle with radius 1 cm?

The circumference is $$C = 2\text{π}(1) = 2\text{π} \text{ cm}$$ .

If a ladybug walks $$\frac{1}{2}$$ of a rotation on a circle with radius 5 cm, what is the distance traveled?

The distance traveled is $$s = 5 \times \frac{1}{2} \times 2\text{π} = 5\text{π} \text{ cm}$$ .

What is the angle in radians for a full rotation?

The angle in radians for a full rotation is $$2\text{π} \text{ rad}$$ .

Radians & Distance Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a radian?

Back

A radian is a unit of angular measure used in mathematics. It is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.

Tags

CCSS.HSF.TF.A.1

2.

FLASHCARD QUESTION

Front

How do you convert degrees to radians?

Back

Tags

CCSS.HSF.TF.A.1

3.

FLASHCARD QUESTION

Front

What is the circumference of a circle with radius r?

Back

Tags

CCSS.7.G.B.4

4.

FLASHCARD QUESTION

Front

If a circle has a radius of 10 cm, what is the distance traveled in one full rotation?

Back

Tags

CCSS.7.G.B.4

5.

FLASHCARD QUESTION

Front

What is the relationship between the distance traveled along a circle and the angle in radians?

Back

Tags

CCSS.HSG.C.B.5

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSG.C.B.5

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.4.MD.C.5B

CCSS.HSG.CO.A.1

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