High School

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For the given central angle, determine the distance traveled along the unit circle from the point (1, 0).

1. 1.57 units clockwise
2. 3.14 units clockwise
3. 1.57 units
4. 3.14 units

Answer :

Final answer:

To calculate the distance traveled on a unit circle for a given central angle, use the arc length formula s = rθ, where s is the arc length, r is the radius of the circle, and θ is the angle in radians. For the unit circle, 1.57 and 3.14 units correspond to approximately a semicircle and a full circle respectively.

Explanation:

The student asked: For the given central angle, determine the distance traveled along the unit circle from the point (1, 0). The options given were 1) 1.57 units clockwise 2) 3.14 units clockwise 3) 1.57 units 4) 3.14 units.

To calculate the distance traveled along the circumference of a unit circle, you utilize the formula s = rθ, where s is the arc length, r is the radius of the circle (which is 1 for a unit circle), and θ represents the angle in radians. Given that the circumference of a unit circle is 2π units, and that 1.57 and 3.14 are approximations of π/2 and π respectively, we can determine the correct distance.

1.57 radians is approximately half of π, so traveling 1.57 units on a unit circle covers a semicircle. Travelling 3.14 radians, which is approximately π, goes around half of the circle twice or a full circle once, thereby covering the entire circumference of the unit circle.

Given that the distance is directly proportional to the angle in a unit circle, the correct answers from the given options would be:

  • 1.57 units (approximately a semicircle traveled counterclockwise from (1, 0))
  • 3.14 units (approximately a full circle traveled counterclockwise from (1, 0))

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