What is a Sine Function?
The sine function (sin x) is a wave-like function, sometimes called a sine wave or sunusoid. It’s type of trigonometric function and is also classified as a periodic function. Trigonometric functions are functions involving angles while periodic functions repeat at set intervals.
It is sometimes called the real sine function to set it apart from it’s complex-valued counterpart.
For the cardinal sine function, see: Sinc Function.
The sine function is trigonometric, which means that it tells you something about circles and angles.
One way to define the sine function is in terms of a triangle. The sine tells you the vertical coordinate of an arc’s endpoint on a unit circle.
In a right angle, the sine is a ratio: the length of the opposite side (O), divided by the hypotenuse. You may remember the familiar acronym SOHCAHTOA: The first part (SOH) deals with the sine: Sine = Opposite / Hypotenuse.
The relationship between the sine and the other parts of a right angle can best explained with a graph:
Domain, Range, and Period of the Sine Function
- The domain is the set of all real numbers.
- The range is from -1 to 1.
- The period of the function sin(x) is 2π.
Real Life Examples
The sine function has many real life applications, a few of which are:
- Triangulation, used in GPS-equipped cellphones,
- Musical notes,
- Submarine depth,
- Length of a zip line,
- Ski slope angle, length and height,
- Directional bearings for pilots, including bearing and distance from a port.
Note that the cosine function can also be used, as sin/cos are so closely related to each other.
Brown, K. Real-Life Applications of Sine and Cosine Functions. Retrieved November 19, 2019 from: https://www.dti.udel.edu/content-sub-site/Documents/curriculum/guide/2013/Thinking%20and%20Reasoning/units/13.02.01.pdf
Larson, R. (2012). Precalculus: Real Mathematics, Real People. Cengage Learning.
Wilson, J. Sine Functions. Retrieved November 29, 2019 from: http://jwilson.coe.uga.edu/EMAT6680Su07/Charlot/Larousses’Bio/sinefunction.htm