Difference between revisions of "Graphs of the Sine and Cosine Functions"

Revision as of 14:32, 22 September 2021

\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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [−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.

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

@@ Line 1: / Line 1: @@
 [[File:Horizontal stretch of sinx.png|thumb|<math> \sin{x} </math> (red) and <math> \sin{\left(\frac{1}{2}x\right)} </math> (green, horizontal stretch of sin(x) by factor of 2). Horizontal stretches/compressions of sine and cosine functions change the period.]]
 [[File:Vertical stretch of sinx.png|thumb|<math> \sin{x} </math> (red) and <math> \sin{\left(2x\right)} </math> (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 <math> (-\infty, \infty) </math> and the range is <math> [−1,1] </math>.
+* The graph of <math> y = \sin{x} </math> is symmetric about the origin.
+* The graph of <math> y = \cos{x} </math> is symmetric about the y-axis.
 ==Resources==
 * [https://mathresearch.utsa.edu/wikiFiles/MAT1093/Graphs%20of%20the%20Sine%20and%20Cosine%20Functions/Esparza%201093%20Notes%202.4.pdf Graphs of the Sine and Cosine]. Written notes created by Professor Esparza, UTSA.
 * [https://courses.lumenlearning.com/precalctwo/chapter/graphs-of-the-sine-and-cosine-function/ Graphs of the Sine and Cosine Functions], Lumen Learning