Math Essay Example | Topics and Well Written Essays - 1000 words - 1

Math - Essay Example Therefore, conjecture, the graphs of the sine function and its derivative cosine function are sinusoids of different phases i.e. the derivative is also a sine function with a phase-shift of (or) is true. For making graph of above sine function and its derivative functions, there will be need of taking value of constant ‘a’. In general, the ‘a’ is called as amplitude of the function. Figure 3 shows the different graphs of sine function and its derivative function for different values of ‘a’ (i.e. 2, 3, and 5). From above figure 3, it is obvious that the graphs of the sine and it derivative cosine functions (for different values of ‘a’) are sinusoids of different phases. The derivative is also a sine function with a phase-shift of (or). Here, the constant ‘a’ (amplitude) different values only change the shape of the sine and cosine functions. As the value of ‘a’ (either positive or negative) increases the shape of the curve will also changes and it goes far from x-axis. The above conjecture for can be verified by graphing similarly as verified for earlier, as shown in figure 2. For same values of constant ‘a’, all the graphs of function, and will be similar and will follows the same path. Therefore, it can be said that all the functions represent the same function, which is derivative of function. From table 2 it is obvious that all values for derivative functions are same (3rd, 4th and 5th column). Therefore, conjecture, the graphs of the sine function and its derivative cosine function are sinusoids of different phases i.e. the derivative is also a sine function with a phase-shift of (or) is true. From figure 1 and figure 4, it can be seen that as the value of b increases, the number of cycle for and for, also increases. For b = 1 the number of cycle is 2, and for b = 2, 3, and 5 the number of cycle is 4, 6 and 10 respectively. In addition, for derivative functions the amplitude