Sine Function Definition Math

The amplitude a is the distance measured from the y value of a horizontal line drawn through the middle of the graph or the average value to the y value of the highest point of the sine curve and b is the number of times the sine curve repeats itself within 2π or 360 degrees.

Sine function definition math. The sine function along with cosine and tangent is one of the three most common trigonometric functions. In a formula it is written as sin without the e. For the specified angle it is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle the hypotenuse. Free math lessons and math homework help from basic math to algebra geometry and beyond.

From a triangle given any angle q 0 q 90 we can find the sine of that angle by constructing a right triangle with one vertex of angle q. It was used in ancient greece and india and in 1140 r. The sine of an acute angle is defined in the context of a right triangle. In terms of right triangles and in terms of the unit circle.

There are two main ways in which trigonometric functions are typically discussed. The graph of the function y a sin bx has an amplitude of a and a period of. Introduction to the sine function. In any right triangle the sine of an angle x is the length of the opposite side o divided by the length of the hypotenuse h.

De chesters translated abu ja far muhammed ibn musa al khwarizme s works and used the word sine in latin sinus. Defining the sine function. In mathematics the sine is a trigonometric function of an angle. Students teachers parents and everyone can find solutions to their math problems instantly.

In this way we can find the sine of any q in the range 0 q 90. Sine written as sin θ is one of the six fundamental trigonometric functions.