Question

Which of the following statements is true concerning the conversion between degree and radian measure? A) To convert from radians to degrees, multiply by 360 degrees and divide by π (pi). B) To convert from radians to degrees, multiply by 180 degrees and divide by π (pi). C) To convert from degrees to radians, multiply by π (pi) and divide by 180 degrees. D) To convert from degrees to radians, multiply by π (pi) and divide by 360 degrees.

Answer 1

AI-generated answer

To convert between degree and radian measure, the following statement is true:

B) To convert from radians to degrees, multiply by 180 degrees and divide by π (pi).

When converting from radians to degrees, we multiply the given value by 180 degrees and then divide by π (pi). This is because one complete revolution is equal to 360 degrees or 2π radians. To find the degree measure of an angle given in radians, we can use the formula:

Degree measure = (Radian measure × 180 degrees) ÷ π (pi)

For example, let's say we have an angle of π/3 radians. To convert it to degrees, we multiply π/3 by 180 degrees and divide by π:

Degree measure = (π/3 × 180 degrees) ÷ π

= (π × 180 degrees) ÷ (3π)

= 180 degrees ÷ 3

= 60 degrees

Therefore, an angle of π/3 radians is equal to 60 degrees.

Remember, radians and degrees are two different units used to measure angles. Radians are used in trigonometry and calculus, while degrees are more commonly used in everyday life.Answer:

Explanation: