It's extremely evident from the first time we meet Rosalind in Act 1, Scene 2 that she feels extremely sad due to the loss of her father and that she is using her wit to hide her sorrow at Celia's request.
Celia opens the very second scene of the play by begging Rosalind, the cousin that she loves, to "be merry" (1). Rosalind's response is to say that she constantly acts like she is happier than she actually is. She further states that unless she can forget about her father who is banished, Celia shouldn't teach her "how to remember any extraordinary pleasure" (6-7). Celia continues to coax her to be happy, pleading that if Rosalind truly loves her, then Rosalind will be happy in the mere fact that they are still together, despite Rosalind's father's banishment. Celia further coaxes her by promising to give Rosalind the dukedom once Celia, as Frederick's only child, inherits it from her father Frederick who has usurped the dukedom from Rosalind's father. From henceforth, Rosalind promises to be happy and amusing and certainly does behave in a happy, amusing, witty way throughout the rest of the play, despite the fact that her father is banished and despite the fact that she herself is soon banished along with him. In fact, Rosalind and Celia make a sort of game out of their banishment, deciding that Rosalind should travel to the Forest of Arden dressed as a man and Celia dressed as a poor peasant. Even when they are both weary from their travels, Rosalind uses her wit to enliven their spirits, jokingly saying that she could "cry like a woman" but must comfort Celia as the "weaker vessel" (II.iv.5-6). The irony is that of course both Rosalind and Celia are the "weaker vessel," showing us just exactly how Rosalind is using her wit to help them through their tribulations as well as any sorrows that both she and Celia are feeling. Hence, Rosalind uses her wit to cover her heartache by using it to bolster both her spirits as well as Celia's.
rosalind needs to keep up a facade because she thinks her sadness hurts her sister she knows that she will not be meeting her father anytime soon but for her sister's sake uses her intelligence and wit to disguise her inner sadness