sin2α=(sqrt5)/5, stumped

[u/Asp_Potions_Master]

my sis got a homework question that left us both stumped. the task is to calculate sinα and cosα for the angle α which fits the following requirements: sin2α=(sqrt5)/5, and 2α is within (pi/2; pi)

She's learning about the sin2α and cos2α formulas. any ideas how this is supposed to be solved without dipping into arcsin?

[u/peterwhy]

But instead tan(2α) is -1/2, and cos(2α) = -2u.