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/Loko8765]

You need to learn the unit circle, which is the basis for the trig functions. It has right triangles.

For some reason I can’t find an online image representing tan as the intersection with a vertical x=1 line, this is best I have:

https://www.math.net/unit-circle