1 and sine function have many important properties and uses. First of all, the sine function is a periodic function with a period of 2π, that is, the function value repeats every 2π. Secondly, the sine function is odd function, that is, f(-x)=-f(x). In addition, the sine function has symmetry, that is, for any real number k, there is f(x+2kπ)=f(x).
2. In the trigonometric function table, you can find the values of sine function at different angles. For example, SIN 30 = 1/2, SIN 45 = √ 2/2, SIN 60 = √ 3/2 and so on. These values are obtained according to Pythagorean theorem and the triangle relationship in the unit circle.
3. Sinusoidal functions are widely used in physics, engineering and economy. For example, in physics, sine function is used to describe the voltage and current waveforms of alternating current; In engineering, sine function is used to describe oscillation and fluctuation; In economics, sine function is used to describe economic data that changes periodically.
Related knowledge of trigonometric functions
1, trigonometric function is a function with angle as independent variable and side length ratio corresponding to angle as function value. The sine function sin(x) is defined as the sine value of any angle x in the unit circle, that is, the ratio of ordinate y to abscissa r, and the cosine function cos(x) is defined as the cosine value of any angle x in the unit circle, that is, the ratio of abscissa r to ordinate y.
2. Trigonometric functions have periodicity, parity, symmetry and boundedness. Among them, sine function and cosine function are both periodic functions with a period of 2π; The tangent function is not a periodic function. Trigonometric functions are all odd function, that is, f(-x)=-f(x). In addition, trigonometric functions have symmetry, for example, sine function takes the maximum value on the symmetry axis, and cosine function oscillates between adjacent symmetry axes.
3. Trigonometric functions are widely used in mathematics, physics, engineering and economy. For example, in mathematics, trigonometric functions can be used to solve plane geometry problems, analytic geometry problems and complex number problems. In physics, trigonometric functions are used to describe wave phenomena, voltage and current waveforms of alternating current, etc.