# C Programming (Turbo / Visual C++ Compiler) - Using Sine and Cosine Series to find TAN Value

I have given here a C program to find the value of TAN using Sine & cosine Series and without using the library function. This program will print the values got from the series function MyTan and library function tan.

sine series = x - x^3/3! + x^5/5! - x^7 / 7! + x^9 / 9! - .......

cosine series = 1 - x^2/2! + x^4/4! - x^6 / 6! + X^8 / 8! - ....

Tan Series = sine series / cosine series

## Source Code

#include <math.h>

#include <stdio.h>

const double PI = 3.14159265;

// tan series = sine series / cosine series

double MyTan(double x)

{

double sineresult = x;

double cosineresult = 1;

double sqx = 0;

double fact = 0;

int index = 0;

int term = 0;

double termfactor = 0;

{

sqx = x * x * x;

fact = 2 * 3;

index = 3;

for(term = 1; term < 20; term++)

{

termfactor = 0;

termfactor = sqx / fact;

if(term % 2)

{

sineresult = sineresult - termfactor;

}

else

{

sineresult = sineresult + termfactor;

}

index++;

fact *= index;

index++;

fact *= index;

sqx *= (x*x);

}

}

{

sqx = x * x;

fact = 2;

index = 2;

for(term = 1; term < 20; term++)

{

termfactor = 0;

termfactor = sqx / fact;

if(term %2)

{

cosineresult = cosineresult - termfactor;

}

else

{

cosineresult = cosineresult + termfactor;

}

index++;

fact *= index;

index++;

fact *= index;

sqx *= (x*x);

}

}

return sineresult / cosineresult;

}

int main()

{

double i = 0;

for(i = 0; i <= 360; i += 4.75)

{

printf("%.4lf = %.4lf\t%.4lf\n", i,

tan(i * PI / 180), MyTan(i * PI / 180));

//printf("%.4lf\n", tan(i * PI / 180) - MyTan(i * PI / 180));

}

return 0;

}

## Output

0.0000 = 0.0000 0.0000

4.7500 = 0.0831 0.0831

9.5000 = 0.1673 0.1673

14.2500 = 0.2540        0.2540

19.0000 = 0.3443        0.3443

23.7500 = 0.4400        0.4400

28.5000 = 0.5430        0.5430

33.2500 = 0.6556        0.6556

38.0000 = 0.7813        0.7813

42.7500 = 0.9244        0.9244

47.5000 = 1.0913        1.0913

52.2500 = 1.2915        1.2915

57.0000 = 1.5399        1.5399

61.7500 = 1.8611        1.8611

66.5000 = 2.2998        2.2998

71.2500 = 2.9459        2.9459

76.0000 = 4.0108        4.0108

80.7500 = 6.1402        6.1402

85.5000 = 12.7062       12.7062

90.2500 = -229.1818     -229.1818

95.0000 = -11.4301      -11.4301

99.7500 = -5.8197       -5.8197

104.5000 = -3.8667      -3.8667

109.2500 = -2.8636      -2.8636

114.0000 = -2.2460      -2.2460

118.7500 = -1.8228      -1.8228

123.5000 = -1.5108      -1.5108

128.2500 = -1.2685      -1.2685

133.0000 = -1.0724      -1.0724

137.7500 = -0.9083      -0.9083

142.5000 = -0.7673      -0.7673

147.2500 = -0.6432      -0.6432

152.0000 = -0.5317      -0.5317

156.7500 = -0.4296      -0.4296

161.5000 = -0.3346      -0.3346

166.2500 = -0.2447      -0.2447

171.0000 = -0.1584      -0.1584

175.7500 = -0.0743      -0.0743

180.5000 = 0.0087       0.0087

185.2500 = 0.0919       0.0919

190.0000 = 0.1763       0.1763

194.7500 = 0.2633       0.2633

199.5000 = 0.3541       0.3541

204.2500 = 0.4505       0.4505

209.0000 = 0.5543       0.5543

213.7500 = 0.6682       0.6682

218.5000 = 0.7954       0.7954

223.2500 = 0.9407       0.9407

228.0000 = 1.1106       1.1106

232.7500 = 1.3151       1.3151

237.5000 = 1.5697       1.5697

242.2500 = 1.9007       1.9007

247.0000 = 2.3559       2.3559

251.7500 = 3.0326       3.0326

256.5000 = 4.1653       4.1653

261.2500 = 6.4971       6.4971

266.0000 = 14.3007      14.3007

270.7500 = -76.3900     -76.3900

275.5000 = -10.3854     -10.3854

280.2500 = -5.5301      -5.5301

285.0000 = -3.7321      -3.7321

289.7500 = -2.7852      -2.7852

294.5000 = -2.1943      -2.1943

299.2500 = -1.7856      -1.7856

304.0000 = -1.4826      -1.4826

308.7500 = -1.2460      -1.2460

313.5000 = -1.0538      -1.0538

318.2500 = -0.8925      -0.8925

323.0000 = -0.7536      -0.7536

327.7500 = -0.6310      -0.6310

332.5000 = -0.5206      -0.5206

337.2500 = -0.4193      -0.4193

342.0000 = -0.3249      -0.3249

346.7500 = -0.2355      -0.2355

351.5000 = -0.1495      -0.1495

356.2500 = -0.0655      -0.0655

Press any key to continue . . .