1 and the derivation of sine sum angle formula;
sin(c)=sin(a+ b).
According to the addition formula of trigonometric function, sin(a+ b) can be expanded as:
sin(a+ b)=sinacosb+ cosasinb .
sin(c)= sin(a+b)= Sina cosb+cosa sinb .
2. Derivation of cosine and angle formulas;
cos(c)=cos(a+ b).
According to the addition formula of trigonometric function, cos(a+ b) can be expanded as:
cos(a+ b)=cosacosb- sinasinb .
cos(c)= cos(a+b)= cosa cosb-Sina sinb .
Application of trigonometric function;
1, the field of signal processing.
In the field of signal processing, trigonometric functions are widely used in signal modulation and demodulation. For example, in AM (amplitude modulation) and FM (frequency modulation) broadcasting, the audio signal will be modulated according to the frequency of the carrier signal, and the carrier signal is a sine wave. Using trigonometric function, we can convert audio signal into sine wave, and then modulate this sine wave with carrier signal, so as to realize the purpose of transmitting signal in broadcasting.
2. Physical field.
In the field of physics, trigonometric functions are widely used in the study of various periodic motions. For example, when studying simple harmonic vibration, physical quantities such as displacement, velocity and acceleration of vibration can be described by trigonometric functions. By using trigonometric function, we can better understand the laws and characteristics of simple harmonic vibration, so as to better predict and control this motion.
3. The field of mathematics.
In the field of mathematics, trigonometric functions are widely used to solve various mathematical problems. For example, when solving the area and perimeter of circles, sectors and arches, trigonometric functions can be used to calculate the parameters and dimensions of these shapes. When solving some analytic geometry problems, trigonometric functions can also be used for coordinate transformation and graphic transformation.