# How to Use This Software

### 1. You can input an angle in radians, and click sine, cosine or atan button to get the value and the estimation error.

### 2. In this calculation, the following polynomials are used to approximate the sine and cosine functions:

Above, Taylor polynomials are used at the point 0 and 2.1, respectively, to obtain a more accurate approximation.

### 3. Because the sine and cosine are periodic functions, the following equation is used to reduce from any input to [-3.14,3.14]:

For atan function, Remez's algorithm is used to calculate the coefficients using the following equations:
### 4. The following equations are used to approximate the arctangent function:

### 5. The error is calculated by the following equation:

### error=p(x)-Math.sin(x)/cos(x)/atan(x)

### References:

[1] J.M. MULLER,*"Elementary functions: Algorithms and implementation"*,Birkbauser,1997.

[2] I. Koren,*"Computer Arithmetric Algorithms"*,A.K. Peters,2002

[3] http://www.mathworks.com/help/matlab/index.html