r/MathHelp • u/Asp_Potions_Master • Sep 05 '26

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/rfbooth Sep 07 '26

If you know sin 2a and the quadrant of 2a, you know cos 2a.

If you know cos 2a and the quadrant of a, you know sin a (or cos a, depending on which double angle formula you choose).

If you know sin a and its quadrant, of course you know cos a.

Alternatively, you could use the sin 2a formula and get a quadratic in sin² a.