Final answer:
To convert 115 degrees to radians, multiply the angle by π/180 to obtain (115π)/180 radians. This is part of the process of converting angular measures from degrees to radians, which is essential in various mathematical applications.
Step-by-step explanation:
To convert from degrees to radians, we use the relationship that one revolution, which is 360 degrees, is equal to 2π radians. This relation is essential because it allows us to set up a proportion to convert degrees into radians. The given angle here is 115 degrees, which we want to convert into radians.
First, let's write down our conversion factor. Since 360 degrees are equivalent to 2π radians, we can express this relationship as:
1 degree = π/180 radians. Now, using this conversion factor, we can convert 115 degrees to radians.
To perform the conversion, we multiply 115 degrees by the conversion factor (π/180 radians per degree):
115 degrees x (π/180 radians/degree) = (115π)/180 radians.
Upon simplifying the multiplication, we will have our answer in radians. Remember, it is crucial to express the π symbol or use the approximate value of 3.14159 when calculating the answer.
Angular velocity is also a related concept, defined as the rate of change of an angle, usually expressed in radians per second. However, it is important to note that for the purpose of this conversion, we are solely focused on transforming the unit of an angular measurement, not calculating angular velocity.