Understanding the Basics of the Sine Function: Exploring the Equation y = sin(x) and its Graph

y = sin (x)

To begin, it’s important to understand the basics of the trigonometric function ‘sine’ (sin)

To begin, it’s important to understand the basics of the trigonometric function ‘sine’ (sin). The sine function relates an angle of a right triangle to the ratio of the length of the side opposite that angle to the length of the hypotenuse (the longest side, which is always opposite the right angle).

Now, let’s break down the equation y = sin(x):

– ‘y’ represents the output or dependent variable.
– ‘sin’ is a trigonometric function indicating we are dealing with the sine of an angle.
– ‘x’ is the input or independent variable, typically representing an angle in degrees or radians.

In this equation, we are assigning the value of sin(x) to y. In other words, for every value of x, y will take on the value of the sine of x.

The sine function can take any real number as an input, and it outputs a value between -1 and 1. This means that for each value of x, y varies between -1 and 1 based on the value of the sine of x.

To further understand the behavior of y = sin(x), we can look at its graph. On a coordinate plane, where the x-axis represents the angle (x) and the y-axis represents the value of sine (y), the graph of y = sin(x) forms a wave-like pattern called a sine wave.

The graph starts at the origin (0, 0), then goes upwards, reaching its highest point at (π/2, 1). It descends back to the x-axis at (π, 0), continues below the x-axis, and hits its lowest point at (3π/2, -1). This pattern repeats infinitely in both the positive and negative x directions.

The amplitude of the sine wave is always 1, which represents the distance of the highest and lowest points from the x-axis. The period of the function, which is the length of one complete wave, is 2π radians or 360 degrees.

In summary, y = sin(x) is an equation representing the value of the sine function for any given angle x. Its graph forms a periodic wave-like pattern, oscillating between -1 and 1.

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