Question

Starting from \theta =-(\pi )/(2), how long does it take (in radians ) before those the value of ( y)/(x) starts to repeat?

Answer 1

It takes 2π radians for the ratio (y)/(x) to start repeating, due to the periodic nature of the sine function with a period of 2π radians.

Step-by-step explanation:

The question asks how long it takes in radians before the value of (y)/(x) starts to repeat from the starting angle of -(π)/(2). The repetition of a function such as the sine function, which is implied in the context, occurs every 2π radians. This is because the sine function is periodic with a period of 2π radians, meaning that the sine function will produce the same values at intervals of 2π radians. Therefore, starting from -(π)/(2), one full period later would be at -(π)/(2) + 2π radians, which simplifies to (π)/(2) + 2π radians. Thus, it takes 2π radians for the value of (y)/(x) to start repeating.