Question

At what point does the sine function y = sin x, cross the y axis?

Answer 1

The sine function
`\(y = \sin x\)` crosses the y-axis at the point
`\((0, 0)\).`

Step-by-step explanation:

The sine function, denoted as
`\(y = \sin x\),` represents a periodic oscillation between -1 and 1 as
`\(x\)` varies. The point where the sine function crosses the y-axis corresponds to
`\(x = 0\)` . Substituting
`\(x = 0\)` into the function yields
`\(y = \sin 0 = 0\).` Therefore, the sine function crosses the y-axis at the point
`\((0, 0)\).`

Understanding the behavior of the sine function is crucial in trigonometry and calculus. The sine function is periodic with a period of
`\(2\pi\)` , meaning it repeats its values every
`\(2\pi\)` units. At
`\(x = 0\)` , the sine function has a zero value, indicating that it crosses the y-axis. As
`\(x\)` increases or decreases in multiples of
`\(2\pi\),` the function continues to cross the y-axis at other points.

The point
`\((0, 0)\)` is significant in the context of trigonometry, as it corresponds to the initial angle in the unit circle. The sine of this angle is
`\(0\),` leading to the intersection of the sine function with the y-axis. This point is foundational in trigonometric concepts and serves as a reference for understanding the behavior of trigonometric functions.