Convert $$\text{π}/2$$ radians to degrees.

$$\text{π}/2$$ radians is equal to 90 degrees.

If the radius of a circle is 5 units and the angle is $$\text{π}/4$$ radians, what is the arc length?

Using the formula $$s = r \theta$$ , the arc length is $$s = 5 \times \frac{\text{π}}{4} = \frac{5\text{π}}{4}$$ units.

If the radius of a circle is 10 units and the angle is 60 degrees, what is the arc length?

Using the formula $$s = \frac{\theta}{360} \times 2\text{π}r$$ , the arc length is $$s = \frac{60}{360} \times 2\text{π} \times 10 = \frac{1}{6} \times 20\text{π} = \frac{10\text{π}}{3}$$ units.

What is the circumference of a circle in terms of radians?

The circumference (C) of a circle can be expressed as $$C = 2\text{π}r$$ , where r is the radius.

What is the formula to convert degrees to radians?

To convert degrees to radians, use the formula: $$\text{radians} = \text{degrees} \times \frac{\text{π}}{180}$$ .

What is the formula to convert radians to degrees?

To convert radians to degrees, use the formula: $$\text{degrees} = \text{radians} \times \frac{180}{\text{π}}$$ .

If an arc length is 8π yd and the radius is 4 yd, what is the angle in radians?

Using the formula $$s = r \theta$$ , the angle is $$\theta = \frac{s}{r} = \frac{8\text{π}}{4} = 2\text{π}$$ radians.

If an arc length is 15π yd and the angle is 90 degrees, what is the radius?

Using the formula $$s = \frac{\theta}{360} \times 2\text{π}r$$ , the radius is $$r = \frac{s \times 360}{\theta \times 2\text{π}} = \frac{15\text{π} \times 360}{90 \times 2\text{π}} = 30 yd$$ .

What is the significance of the angle in radians when calculating arc length?

The angle in radians directly relates to the proportion of the circle's circumference that the arc length represents, making it essential for accurate calculations.

Radians/Degrees/ArcLength 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 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 many degrees are in one radian?

Back

One radian is approximately 57.2958 degrees.

Tags

CCSS.HSF.TF.A.1

3.

FLASHCARD QUESTION

Front

What is the formula for arc length in radians?

Back

Tags

CCSS.HSG.C.B.5

4.

FLASHCARD QUESTION

Front

What is the formula for arc length in degrees?

Back

Tags

CCSS.HSG.C.B.5

5.

FLASHCARD QUESTION

Front

Convert 180 degrees to radians.

Back

Tags

CCSS.HSF.TF.A.1

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.A.1

7.

FLASHCARD QUESTION

Front

What is the relationship between degrees and radians?

Back

Tags

CCSS.HSF.TF.A.1

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