Raise your vanguard lvl to lvl 2 and buy legendary fron your mentor its faster and less hassle.

I've only gotten two legendary armor pieces and I had to grind for days to get them. Farming spinmetal/spirit bloom/etc... and turning them in to the Vanguard dealer in the hanger, doing Vanguard Bounties, getting gold in a public event each day, playing the Strike Playlist, and doing patrol missions. All for Vanguard rank and marks. I've been a level 25 for a few days and I've never once even seen a legendary engram in my nearly 3 days of playtime. Maybe you should try to get them the proper way and not rely on pure chance and blind luck. I obviously don't have either and am just dealing with the slow and steady way that is intended on a game of this nature. Plenty of ways to get legit rep and marks. Plus the bonus of picking what you want versus leaving it all to chance.

I feel you, I've been on level 24 for 4 days, today would have been the fifth. Finally reached lvl 25, but only because I bought exotic gauntlets from Xur. This game can be really frustrating sometimes.

It may not be the quickest way to get one, but if you want a guaranteed legendary weapon/armor, all you have to do is get vanguard/crucible/FWC/dead orbit/ or new monarchy reputation and marks. If you buy them from vendors, you are always sure you're getting the kind of weapon/armor you want as well.

Yes, the only way to get a guaranteed legendary is by spending crucible/vanguard marks at the NPCS in the tower after you have some reputation with them

There's really nothing you can do to change it or fix it just get as many engrams as you can and hope for the best and dont forget rare engrams can also give you legendary stuff I already got 2 legendary chest plates from rare engrams so really it all boils down to luck