Find a Coterminal Angle between 0o and 360o: -55o
Understanding angles and their measurements is a fundamental concept in trigonometry. One of the key concepts in this field is coterminal angles. A coterminal angle is an angle that has the same initial and terminal sides as another angle, but differs by a multiple of 360 degrees. In this article, we will explore how to find a coterminal angle between 0o and 360o for the given angle of -55o.
To find a coterminal angle between 0o and 360o for -55o, we need to add or subtract multiples of 360 degrees to the given angle. The goal is to obtain an angle within the specified range. In this case, we want to find an angle between 0o and 360o.
Let’s start by adding 360 degrees to -55o:
-55o + 360o = 305o
The angle 305o is a coterminal angle of -55o, as it has the same terminal side but differs by a multiple of 360 degrees. However, we need to ensure that the coterminal angle is between 0o and 360o. Since 305o is within this range, it is the coterminal angle we are looking for.
In some cases, adding 360 degrees may not yield a coterminal angle within the desired range. In such scenarios, we can continue adding or subtracting 360 degrees until we find an angle between 0o and 360o. For instance, if we add another 360 degrees to 305o:
305o + 360o = 665o
This angle is outside the range of 0o to 360o. To bring it back within the desired range, we can subtract 360 degrees:
665o – 360o = 305o
As we can see, the angle 305o is still within the range of 0o to 360o and is a coterminal angle of -55o.
In conclusion, to find a coterminal angle between 0o and 360o for -55o, we added 360 degrees to the given angle, resulting in 305o. This coterminal angle is within the specified range and can be used for various trigonometric calculations and applications. Understanding coterminal angles is crucial for simplifying trigonometric expressions and solving problems involving angles in different quadrants.
