L3: Radian Measures

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.

Front

How do you convert radians to degrees?

Back

To convert radians to degrees, multiply the radian measure by \(\frac{180}{\pi}\).

Front

What is the formula for the length of an arc?

Back

The length of an arc (s) can be calculated using the formula: \(s = r\theta\), where \(r\) is the radius and \(\theta\) is the angle in radians.

Front

If the radius of a circle is 10 inches and the angle is \(\frac{\pi}{3}\) radians, what is the length of the arc?

Back

The length of the arc is \(s = 10 \times \frac{\pi}{3} = \frac{10\pi}{3} \approx 10.47\) inches.

Front

What is the relationship between degrees and radians?

Back

180 degrees is equal to \(\pi\) radians.

Front

How do you find the circumference of a circle using radians?

Back

The circumference (C) of a circle can be calculated using the formula: \(C = 2\pi r\), where \(r\) is the radius.

Front

What is the angle in radians for a full circle?

Back

A full circle is \(2\pi\) radians.

Front

Convert \(\frac{3\pi}{4}\) radians to degrees.

Back

To convert, multiply by \(\frac{180}{\pi}\): \(\frac{3\pi}{4} \times \frac{180}{\pi} = 135\) degrees.

Front

What is the formula to convert degrees to radians?

Back

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

Front

If an arc length is 15 inches and the radius is 5 inches, what is the angle in radians?

Back

Using the formula \(s = r\theta\), we have \(15 = 5\theta\), so \(\theta = 3\) radians.