What is the general solution to y = arcsin 0?

y= positive or negative pie K

To find the general solution to the equation y = arcsin(0), we first need to understand the properties of the arcsine function. The arcsine function, denoted by sin^(-1)(x) or asin(x), returns the angle whose sine value is x.

In this case, we have y = arcsin(0). The sine value of 0 is 0 for the angle of 0, π, 2π, and so on. However, the arcsine function returns the angle only within a specific range.

The range of the arcsine function is -π/2 to π/2, or -90° to 90°. Therefore, the general solution for y = arcsin(0) is:

y = 0 + kπ, where k is an integer.

This means that y can take on any value that is a multiple of π (or 180°) within the range of -90° to 90°.

The general solution to the equation y = arcsin(0) can be found by understanding the inverse sine function, as well as the concept of angles and their trigonometric functions.

To find the general solution, let's first recall the definition of the inverse sine function (arcsin). The inverse sine function returns the angle whose sine is a given value. In this case, y = arcsin(0), we are looking for the angle whose sine is equal to 0.

The sine function is a periodic function, meaning it repeats itself after every full rotation around the unit circle. The values of sine range from -1 to 1. In the unit circle, the sine is positive in the first and second quadrants, and negative in the third and fourth quadrants.

To find where the sine is equal to 0, we look for the angles where the sine of that angle is 0. These angles can be found at 0 degrees (or 0 radians) and 180 degrees (or π radians).

Therefore, the general solution to y = arcsin(0) is:

y = 0 + nπ
or
y = π + nπ,

where n represents any integer.

In other words, the solution can be any angle that is an integer multiple of π radians (or 180 degrees), including 0, π, 2π, -π, -2π, and so on.

look at the sine curve, it is zero, or crosses the horizontal axis at

0 , ±π , ±2π ..

or in general kπ , where k is an integer.