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

Revision as of 14:27, 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.

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

@@ 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.]]
+==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.