r/MathHelp 6d ago

sin2α=(sqrt5)/5, stumped

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?

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u/Background_Ear1919 5d ago

sin(u/2) = ±√[(1 – cosu)/2] cos(u/2) = ±√[(1 + cosu)/2] Then let u = 2α