Graphs of the Sine and Cosine Functions

$\sin {x}$ (red) and $\sin {\left({\frac {1}{2}}x\right)}$ (green, horizontal stretch of sin(x) by factor of 2). Horizontal stretches/compressions of sine and cosine functions change the period.

$\sin {x}$ (red) and $\sin {\left(2x\right)}$ (green, vertical stretch of sin(x) by factor of 2). Vertical stretches/compressions of sine and cosine functions change the amplitude.

The sine and cosine functions have several distinct characteristics:

• They are periodic functions with a period of 2π.
• The domain of each function is $(-\infty ,\infty )$ and the range is [−1,1].
• The graph of $y=\sin {x}$ is symmetric about the origin.
• The graph of $y=\cos {x}$ is symmetric about the y-axis.

Resources

• Graphs of the Sine and Cosine. Written notes created by Professor Esparza, UTSA.
• Graphs of the Sine and Cosine Functions, Lumen Learning