Graphs of the Sine and Cosine Functions

$\sin {x}$ (red) and 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 \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.

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 \sin{x} } (red) and 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 \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 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 (-\infty, \infty) } and the range is [−1,1].
• The graph of 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 y = \sin{x} } is symmetric about the origin.
• The graph of 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 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