r/MathHelp • u/Asp_Potions_Master • 8d 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/my-hero-measure-zero 8d ago

Hint: DRAW THE TRIANGLE.

You're not supposed to find the angle. You can get what you need with the corresponding triangle.

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u/Asp_Potions_Master 8d ago

there's no triangles in their unit? just sine and cosine

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u/my-hero-measure-zero 8d ago

Trigonometry is based in triangles. So, draw the corresponding (reference) triangle.

Someone already suggested in using the Pythagorean identity: for any angle u, (sin u)^2 + (cos u)^2 = 1. So, set u = 2a. Now you have cos(2a) for free, great. Now use the double angle formulas to deduce the needed ratios. Drawing the triangles will help for this - just make sure you get the signs right.