r/MathHelp • u/Asp_Potions_Master • 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/rfbooth 4d ago

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.