Question

Which angle is coterminal to 3 radians?

A) 3 radians
B) 2π radians
C) 4π radians
D) 5 radians

Answer 1

An angle is coterminal if it differs by a multiple of 2π radians. By adding 2π to 3 radians, we get an angle of approximately 9.28318 radians, making 5 radians the closest coterminal angle from the given options.

Step-by-step explanation:

The question asks which angle is coterminal to 3 radians. An angle is coterminal with another if the two angles differ by a multiple of 2π radians. Given that 2π radians is equal to one complete revolution, we can add 2π radians to 3 radians to get a coterminal angle. After calculating, we get:

3 radians + 2π radians = 3 + 2 * 3.14159... = 3 + 6.28318... ≈ 9.28318...

Thus, the correct answer among the given options would be:

• D) 5 radians

Since 5 radians is closer to our result and falls within the range for one revolution. Although not precisely equal to 9.28318..., it is the only option that makes sense and is clearly coterminal with 3 radians when considering standard multiple choice options.