Table of Contents

## What is a real life example of a sinusoidal function?

Sine and cosine functions can be used to model many real-life scenarios – radio waves, tides, musical tones, electrical currents.

## How do you solve a sinusoidal function?

Match the x position of standard function, e.g. sin(u) is at Max when u=π/2 . Solve the equation of u to get x position , e.g. sin(2x+3) , set 2x+3 = π/2 to get x . x is the x position of the peak point of the initial period ….Peak points (Max & Min)

- sin(x):
- Max: x=π/2.
- Min: x=3π/2.
- cos(x):
- Max: x=0.
- Min: x=π

**What is the sinusoidal formula?**

A sinusoidal function is a function using the sine function. The basic form of a sinusoidal function is y = A sin (B(x – C)) + D, where A is the amplitude or height of our function, B is the change in period defined by 2pi/B, C the horizontal shift, and D the vertical shift.

**What are sinusoidal functions used for?**

For objects that exhibit periodic behavior, a sinusoidal function can be used as a model since these functions are periodic. However, the concept of frequency is used in some applications of periodic phenomena instead of the period.

### How do you use sine and cosine models?

The sine and cosine functions can be used to model fluctuations in temperature data throughout the year. An equation that can be used to model these data is of the form: y = A cos B(x – C) + D, where A,B,C,D, are constants, y is the temperature in °C and x is the month (1–12).

### Why are sinusoidal functions used?

A mathematical model is a function that describes some phenomenon. For objects that exhibit periodic behavior, a sinusoidal function can be used as a model since these functions are periodic. However, the concept of frequency is used in some applications of periodic phenomena instead of the period.

**What are Sinusoids used for?**

The term sinusoidal is used to describe a curve, referred to as a sine wave or a sinusoid, that exhibits smooth, periodic oscillation. It is named based on the function y=sin(x). Sinusoids occur often in math, physics, engineering, signal processing and many other areas.

**How do you find the period of a sinusoidal function?**

We have a really easy way to determine the period of the sine function. If we have a sine function of the form f(x) = Asin(Bx + C) + D, then the period of the function is 2π / |B|.

#### How do you find the equation of a sinusoidal function from a graph?

1 Answer

- •The amplitude of a graph is the distance on the y axis between the normal line and the maximum/minimum.
- •The period of a graph is the distance on the x axis before the function repeats itself.
- •The horizontal displacement is given by solving for x in x−c=0 in y=acosb(x−c)+dory=asinb(x−c)+d .
- •

#### What is sinusoidal function?

A sinusoidal function is one with a smooth, repetitive oscillation. “Sinusoidal” comes from “sine”, because the sine function is a smooth, repetitive oscillation. Examples of everyday things which can be represented by sinusoidal functions are a swinging pendulum, a bouncing spring, or a vibrating guitar string.

**What are the parts of a sinusoidal function?**

Midline, amplitude, and period are three features of sinusoidal graphs.