Question

Вычислите sin2a,cos2a,tg2a,если sinа=1/2

Answer 1

Sin 2α = 2sinαcosα    cos²α = 1 - sin²α = 1 - 1/4 = 3/4   cosα = √3/2

sin2α = 2 * 1/2 * √3/2 = √3/2

cos 2α = cos²α - sin²α = 3/4 - 1/4 = 2/4 = 1/2

tg 2α = 2tg α / ( 1 - tg²α) = (2 * 1/√3) / (1 - 1/3) = 2/√3 * 3/2 = 3/√3