Graphing Sine and Cosine Curves Calculator in Degrees

This calculator helps you graph sine and cosine functions in degrees. You can adjust amplitude, period, phase shift, and vertical shift to visualize different trigonometric curves.

Introduction

Sine and cosine functions are fundamental in trigonometry and have numerous applications in physics, engineering, and computer graphics. Understanding how to graph these functions in degrees is essential for visualizing periodic phenomena.

The general form of a sine function in degrees is:

Sine Function Formula

y = A * sin(B(x - C)) + D

A - Amplitude (peak deviation from center line)
B - Frequency (affects period)
C - Phase shift (horizontal shift)
D - Vertical shift

The cosine function has a similar form but starts at its maximum value:

Cosine Function Formula

y = A * cos(B(x - C)) + D

How to Use the Calculator

Select whether you want to graph sine or cosine
Enter the amplitude (A) - how tall the wave is
Enter the period (T) - how wide the wave is (in degrees)
Enter the phase shift (C) - horizontal shift of the wave
Enter the vertical shift (D) - vertical position of the wave
Click "Calculate" to generate the graph
Click "Reset" to clear all inputs

Note

The calculator uses degrees for all angle measurements. The period is calculated as 360° divided by the frequency (B).

Formulas

The calculator uses these formulas to generate the graphs:

Sine Function

y = A * sin((360°/T) * (x - C)) + D

Cosine Function

y = A * cos((360°/T) * (x - C)) + D

Where:

A = Amplitude
T = Period (in degrees)
C = Phase shift (in degrees)
D = Vertical shift

Examples

Example 1: Basic Sine Wave

Graph a sine wave with amplitude 2, period 360°, no phase shift, and no vertical shift.

Function: sine
A: 2
T: 360
C: 0
D: 0

This will produce a standard sine wave oscillating between -2 and 2.

Example 2: Shifted Cosine Wave

Graph a cosine wave with amplitude 1.5, period 180°, phase shift of 45°, and vertical shift of 1.

Function: cosine
A: 1.5
T: 180
C: 45
D: 1

This wave will be shifted right by 45° and up by 1 unit.

FAQ

What is the difference between sine and cosine functions?

The sine function starts at zero and reaches its maximum at 90°, while the cosine function starts at its maximum value. Both complete one full cycle over 360°.

How do I change the period of the wave?

The period is determined by the frequency (B). For a sine or cosine function, the period T is calculated as 360° divided by B. A smaller period value makes the wave narrower.

What does amplitude mean in this context?

Amplitude refers to the maximum distance from the center line (y=0) to the peak or trough of the wave. It determines how tall the wave is.