Radians & Distance

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.

Front

How many radians are in a full rotation?

Back

There are 2π radians in a full rotation.

Front

What is the formula to calculate the distance traveled along a circle?

Back

The distance traveled (arc length) can be calculated using the formula: \(d = r \cdot \theta\), where \(d\) is the distance, \(r\) is the radius, and \(\theta\) is the angle in radians.

Front

If a circle has a radius of 10 cm, what is the circumference?

Back

The circumference of a circle is given by the formula: \(C = 2\pi r\). For a radius of 10 cm, \(C = 20\pi\ cm\).

Front

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

Back

The distance traveled is \(16\pi\ cm\).

Front

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

Back

The angle is \(\frac{\pi}{4}\ rad\).

Front

What is the angle in radians if a ladybug walks \(\frac{4}{5}\) of a rotation?

Back

The angle is \(1.6\pi\ rad\).

Front

What is the angle in radians if a ladybug walks 2 rotations?

Back

The angle is \(4\pi\ rad\).

Front

If a circle has a radius of 1 cm, what is the distance traveled if a ladybug walks \(\frac{3}{4}\) of a rotation?

Back

The distance traveled is \(1.5\pi\ cm\).

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, use the formula: \(radians = degrees \cdot \frac{\pi}{180}\).