Convert 300 degrees to radians.
The Correct Answer and Explanation is:
A = 5
B = 3
To convert an angle from degrees to radians, we use the fundamental relationship that defines the two units of angular measurement. A full circle is known to be 360 degrees, which is equivalent to 2π radians. This relationship can be simplified by dividing both sides by 2, giving us the most common conversion identity: 180 degrees equals π radians.
From this core equation, we can derive the conversion factor needed to change any degree measure into radians. If we take the equation 180° = π radians and divide both sides by 180, we find that 1 degree is equal to π/180 radians. Consequently, to convert any given angle from degrees to radians, we must multiply the degree value by this conversion factor, π/180.
For this specific problem, we need to convert 300 degrees into radians. We apply the formula by multiplying 300 by π/180:
Radians = 300 × (π / 180)
This calculation gives us the expression (300π / 180) radians. The next crucial step is to simplify the fraction 300/180 to its simplest form. A straightforward way to start is by dividing both the numerator and the denominator by 10, which reduces the fraction to 30/18.
Now, we need to simplify 30/18 further. We look for the greatest common divisor (GCD) of 30 and 18, which is the largest number that divides both of them without a remainder. The GCD of 30 and 18 is 6. Dividing both the numerator and the denominator by 6, we get:
30 ÷ 6 = 5
18 ÷ 6 = 3
This simplifies the fraction to 5/3. Therefore, 300 degrees is equivalent to 5π/3 radians.
The problem requires the answer to be in the form (A/B)π rad. By comparing our final answer, 5π/3 radians, with the given format, we can determine the values for A and B. The numerator, A, is 5, and the denominator, B, is 3.
