Trigonometric ratios are important tools for understanding how waves move in physics. When we study waves, we use special functions called sinusoidal functions, which involve sine and cosine. For example, the movement of a wave can be described by the equation below:

$$y(x, t) = A \sin(kx - \omega t)$$

In this equation:

• $A$ means the amplitude (how high the wave reaches)
• $k$ stands for the wave number (how many waves fit in a certain space)
• $\omega$ refers to the angular frequency (how fast the wave moves)

The sine function helps us see how the wave changes over time.

Real-World Uses

1. Sound Waves: Sound travels through the air as changes in pressure. We can use trigonometric ratios to figure out their frequency (how often they happen) and wavelength (how long each wave is).

2. Light Waves: When we study light waves, we use sine and cosine to describe how they move, how they interfere with each other, and how they spread out.

By using trigonometric ratios, we can predict how waves will behave. This knowledge is very important in areas like physics and engineering.