Please read 1 Cor.11 looking up covered and uncovered every place it is used.You will see it has three or four different meanings.
http://www.sacred-texts.com/bib/poly/co1011.htm
KJV
1 Be1096 ye followers3402 of me,3450 even as2531 I also2504 am of Christ.5547
2 Now1161 I praise1867 you,5209 brethren,80 that3754 ye remember3415 me3450 in all things,3956 and2532 keep2722 the3588 ordinances,3862 as2531 I delivered3860 them to you.5213
3 But1161 I would2309 have you5209 know,1492 that3754 the3588 head2776 of every3956 man435 is2076 Christ;5547 and1161 the head2776 of the woman1135 is the3588 man;435 and1161 the head2776 of Christ5547 is God.2316
4 Every3956 man435 praying4336 or2228 prophesying,4395 having2192 his head covered,2596 2776 dishonoreth2617 his848 head.2776
5 But1161 every3956 woman1135 that prayeth4336 or2228 prophesieth4395 with her head2776 uncovered177 dishonoreth2617 her1438 head:2776 for1063 that is2076 even all one1520 2532 848 as if she were shaven.3587
6 For1063 if1487 the3588 woman1135 be not3756 covered,2619 let her also2532 be shorn:2751 but1161 if1487 it be a shame149 for a woman1135 to be shorn2751 or2228 shaven,3587 let her be covered.2619
7 For1063 a man435 indeed3303 ought3784 not3756 to cover2619 his head,2776 forasmuch as he is5225 the image1504 and2532 glory1391 of God:2316 but1161 the woman1135 is2076 the glory1391 of the man.435
8 For1063 the man435 is2076 not3756 of1537 the woman;1135 but235 the woman1135 of1537 the man.435
9 1063 Neither2532 3756 was the man435 created2936 for1223 the3588 woman;1135 but235 the woman1135 for1223 the3588 man.435
10 For this cause1223 5124 ought3784 the3588 woman1135 to have2192 power1849 on1909 her head2776 because1223 of the3588 angels.32
11 Nevertheless4133 neither3777 is the man435 without5565 the woman,1135 neither3777 the woman1135 without5565 the man,435 in1722 the Lord.2962
12 For1063 as5618 the3588 woman1135 is of1537 the3588 man,435 even so3779 is the3588 man435 also2532 by1223 the3588 woman;1135 but1161 all things3956 of1537 God.2316
13 Judge2919 in1722 yourselves:5213 846 is2076 it comely4241 that a woman1135 pray4336 unto God2316 uncovered?177
14 Doth2228 not even3761 nature5449 itself846 teach1321 you,5209 that,3754 if1437 a man435 have long hair,2863 it is2076 a shame819 unto him?846
15 But1161 if1437 a woman1135 have long hair,2863 it is2076 a glory1391 to her:846 for3754 her hair2864 is given1325 her846 for473 a covering.4018
16 But1161 if1487 any man5100 seem1380 to be1511 contentious,5380 we2249 have2192 no3756 such5108 custom,4914 neither3761 the3588 churches1577 of God.2316