sine, cosine, tangentを日本語で、正弦、余弦、正接という
tanは45°で1, 30°で√3/3
#include 
#include 
int main(void){
	int thd;
	double th;
	FILE *fp = NULL;
	char c[128];
	fp=fopen("tangent.txt", "w");
	if(fp == NULL) return 1;
	fputs("正接表\n\n", fp);
	fputs("角度\t正接\n",fp);
	printf("\n角度\t正接\n");
	for(thd=-89; thd<90; thd+=1){
		th = thd*0.017453295;
		sprintf(c, "%3d\t%10.6f\n",thd, tan(th));
		fputs(c,fp);
		printf("%s",c);
	}
	if(fp!=NULL) fclose(fp);
	return 0;
}
$ gcc -o main main.c
/tmp/cc1hB26c.o: In function `main':
main.c:(.text+0xe1): undefined reference to `tan'
あれ? tanは特にincludeは要らないはずだが。
stackoverflowに買いてありますな。
You should add -lm to your compiler option.
Besides of that, you could also change -lpthread to -pthread.
$ gcc -o main main.c -lm
$ ./main
角度	正接
-89	-57.290686
-88	-28.636432
-87	-19.081215
-86	-14.300710
-85	-11.430080
-84	 -9.514384
-83	 -8.144360
-82	 -7.115380
-81	 -6.313760
-80	 -5.671288
-79	 -5.144559
-78	 -4.704635
-77	 -4.331480
-76	 -4.010784
-75	 -3.732054
-74	 -3.487417
-73	 -3.270855
-72	 -3.077685
-71	 -2.904213
-70	 -2.747479
-69	 -2.605090
-68	 -2.475088
-67	 -2.355853
-66	 -2.246038
-65	 -2.144508
-64	 -2.050305
-63	 -1.962611
-62	 -1.880727
-61	 -1.804048
-60	 -1.732051
-59	 -1.664280
-58	 -1.600335
-57	 -1.539865
-56	 -1.482561
-55	 -1.428148
-54	 -1.376382
-53	 -1.327045
-52	 -1.279942
-51	 -1.234897
-50	 -1.191754
-49	 -1.150369
-48	 -1.110613
-47	 -1.072369
-46	 -1.035531
-45	 -1.000000
-44	 -0.965689
-43	 -0.932515
-42	 -0.900404
-41	 -0.869287
-40	 -0.839100
-39	 -0.809784
-38	 -0.781286
-37	 -0.753554
-36	 -0.726543
-35	 -0.700208
-34	 -0.674509
-33	 -0.649408
-32	 -0.624869
-31	 -0.600861
-30	 -0.577350
-29	 -0.554309
-28	 -0.531710
-27	 -0.509526
-26	 -0.487733
-25	 -0.466308
-24	 -0.445229
-23	 -0.424475
-22	 -0.404026
-21	 -0.383864
-20	 -0.363970
-19	 -0.344328
-18	 -0.324920
-17	 -0.305731
-16	 -0.286745
-15	 -0.267949
-14	 -0.249328
-13	 -0.230868
-12	 -0.212557
-11	 -0.194380
-10	 -0.176327
 -9	 -0.158384
 -8	 -0.140541
 -7	 -0.122785
 -6	 -0.105104
 -5	 -0.087489
 -4	 -0.069927
 -3	 -0.052408
 -2	 -0.034921
 -1	 -0.017455
  0	  0.000000
  1	  0.017455
  2	  0.034921
  3	  0.052408
  4	  0.069927
  5	  0.087489
  6	  0.105104
  7	  0.122785
  8	  0.140541
  9	  0.158384
 10	  0.176327
 11	  0.194380
 12	  0.212557
 13	  0.230868
 14	  0.249328
 15	  0.267949
 16	  0.286745
 17	  0.305731
 18	  0.324920
 19	  0.344328
 20	  0.363970
 21	  0.383864
 22	  0.404026
 23	  0.424475
 24	  0.445229
 25	  0.466308
 26	  0.487733
 27	  0.509526
 28	  0.531710
 29	  0.554309
 30	  0.577350
 31	  0.600861
 32	  0.624869
 33	  0.649408
 34	  0.674509
 35	  0.700208
 36	  0.726543
 37	  0.753554
 38	  0.781286
 39	  0.809784
 40	  0.839100
 41	  0.869287
 42	  0.900404
 43	  0.932515
 44	  0.965689
 45	  1.000000
 46	  1.035531
 47	  1.072369
 48	  1.110613
 49	  1.150369
 50	  1.191754
 51	  1.234897
 52	  1.279942
 53	  1.327045
 54	  1.376382
 55	  1.428148
 56	  1.482561
 57	  1.539865
 58	  1.600335
 59	  1.664280
 60	  1.732051
 61	  1.804048
 62	  1.880727
 63	  1.962611
 64	  2.050305
 65	  2.144508
 66	  2.246038
 67	  2.355853
 68	  2.475088
 69	  2.605090
 70	  2.747479
 71	  2.904213
 72	  3.077685
 73	  3.270855
 74	  3.487417
 75	  3.732054
 76	  4.010784
 77	  4.331480
 78	  4.704635
 79	  5.144559
 80	  5.671288
 81	  6.313760
 82	  7.115380
 83	  8.144360
 84	  9.514384
 85	 11.430080
 86	 14.300710
 87	 19.081215
 88	 28.636432
 89	 57.290686