There are 2 different methods for sexing a tarantula that is not a mature male. One can be done by looking at a spot on the bottom of the tarantulas abdomen (never really 100% accurate, but can give you a good idea of the sex). Another way is after the tarantula molts, you look at that same spot from the inside of the molt (the spermathecae) and you will notice a flap of skin if it is female, and if there is none then it is male (100% accurate if you know what you are looking for, there are different spermathecae shapes for different species so it can be difficult to look for on some species).

Both of these methods require practice to become accurate and to know what you are looking for. I have been able to sex all of the tarantulas I have had in the past 2 years by spermathecae sexing, and after knowing what to look for it becomes quite easy.

Judging just from that picture the tarantula looks female, I'm only saying this because I do not see mating hooks that a male would have, but without having a molt or knowing if this tarantula is mature or not I can not give you a 100% answer.

My first tarantula was a rose hair, they told me it was female but it molted for me about 2 months after I had it into a mature male. If it is male you will notice that its pedipalps will develop "boxing glove" looking balls to the end of them, and the first set of legs after that will both develop hooks that will be clearly visible.

I have some pictures I'll find for you to show you some hooks and spermathecaes.