Convert 300 degrees to radians.
The Correct Answer and Explanation is:
Correct Answer:
A = 5
B = 3
Explanation:
To convert an angle from degrees to radians, we use the fundamental relationship between these two units of angular measurement. A full circle is 360 degrees, which is equivalent to 2π radians. This relationship can be simplified to its most common form: 180 degrees is equal to π radians.
From this core identity, we can create a conversion factor. To convert from degrees to radians, you multiply the degree measure by the fraction (π / 180°). This works because you are essentially multiplying by a form of 1, as π radians and 180 degrees represent the same amount of rotation. This process, often seen in dimensional analysis, allows the ‘degree’ units to cancel out, leaving the ‘radian’ unit.
The problem asks to convert 300 degrees into radians. Following the conversion method:
Angle in Radians = (Angle in Degrees) × (π / 180°)
Substitute the given value of 300 degrees into the formula:
Angle in Radians = 300 × (π / 180)
This gives us the expression (300π / 180) radians. The next crucial step is to simplify the fraction 300/180 to its lowest terms, as the question requires the answer in the form A/B π, which implies a simplified fraction.
We can simplify 300/180 by finding the greatest common divisor (GCD) for both the numerator (300) and the denominator (180).
First, we can divide both numbers by 10 to remove the trailing zeros:
300 ÷ 10 = 30
180 ÷ 10 = 18
The fraction simplifies to 30/18.
Next, we find the GCD of 30 and 18. Both numbers are divisible by 6.
30 ÷ 6 = 5
18 ÷ 6 = 3
The fully simplified fraction is 5/3.
Therefore, 300 degrees is equivalent to (5/3)π radians.
The problem requires the answer to be in the form (A/B)π rad. By comparing our result, (5/3)π, with this format, we can directly identify the values of A and B.
A is the numerator of the simplified fraction, which is 5.
B is the denominator of the simplified fraction, which is 3.
