HW 4.1 Radians & Degrees

Front

What is the formula for the area of a sector in a circle?

Back

The area of a sector is given by the formula: \( A = \frac{1}{2} r^2 \theta \), where \( r \) is the radius and \( \theta \) is the angle in radians.

Front

How do you convert degrees to radians?

Back

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

Front

What is the relationship between radians and degrees?

Back

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

Front

What is a coterminal angle?

Back

Coterminal angles are angles that share the same terminal side when drawn in standard position. They can be found by adding or subtracting multiples of 360 degrees or \( 2\pi \) radians.

Front

How do you find a coterminal angle for 30 degrees?

Back

To find a coterminal angle, add or subtract 360 degrees. For example, \( 30 + 360 = 390 \) degrees or \( 30 - 360 = -330 \) degrees.

Front

What is the radian measure of 180 degrees?

Back

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

Front

What is the degree measure of an angle with a radian measure of \( \frac{\pi}{3} \)?

Back

The degree measure is 60 degrees.

Front

What direction are negative angles measured from the standard position?

Back

Negative angles are measured clockwise from the standard position.

Front

What is the radian measure of 90 degrees?

Back

90 degrees is equal to \( \frac{\pi}{2} \) radians.

Front

How do you calculate the length of an arc in a circle?

Back

The length of an arc is given by the formula: \( L = r\theta \), where \( r \) is the radius and \( \theta \) is the angle in radians.