Given that sinα = 3/5, we can find cosα using the Pythagorean identity sin²α + cos²α = 1.

cos²α = 1 - sin²α
cosα = √(1 - sin²α)
cosα = √(1 - (3/5)²)
cosα = √(1 - 9/25)
cosα = √(16/25)
cosα = 4/5

Now, we can find sin2α and cos2α using the double angle formulas:

sin2α = 2sinαcosα
sin2α = 2(3/5)(4/5)
sin2α = 24/25

cos2α = cos²α - sin²α
cos2α = (4/5)² - (3/5)²
cos2α = 16/25 - 9/25
cos2α = 7/25

Therefore, sin2α = 24/25 and cos2α = 7/25.