What value between 0 and 360 degrees expresses the same angle as 960 degrees?
The correct answer and explanation is:
To express 960 degrees as an equivalent angle between 0 and 360 degrees, we need to reduce it within one full rotation (360 degrees). The method to do this is by subtracting multiples of 360 degrees from 960 degrees until it falls within the 0 to 360-degree range.
- First, divide 960 by 360 to find how many full rotations it contains: 960÷360=2.6667960 \div 360 = 2.6667 This means 960 degrees consists of 2 full rotations (720 degrees) and some extra angle.
- Now, subtract the total angle of the two full rotations (720 degrees) from 960 degrees: 960−720=240960 – 720 = 240
Thus, the equivalent angle is 240 degrees.
This angle of 240 degrees lies between 0 and 360 degrees, which means it is the same direction as 960 degrees but reduced to a single rotation.
In general, to find an equivalent angle between 0 and 360 degrees for any given angle, you subtract multiples of 360 until the result lies within this range. If the angle is negative, you would add 360 repeatedly until the result is positive and within the desired range.
Understanding this is crucial when dealing with angles in trigonometry and geometry, especially when angles exceed one full rotation. Reducing the angle within 0 to 360 degrees helps in simplifying calculations, especially when analyzing circular motion, periodic functions, or working with bearings.