Question

Oblicz sin(30 + beta) i sin(60 - beta), jeśli:
(a) sinB = 4/5 i B należy do przedziału(0,90 stopni)

Answer 1

Sinβ = 4/5
cosβ = √(1-sin²β) = √[1 - (4/5)²] = √(1 - 16/25) = √(25/25 - 16/25) = √9/25 = 3/5
sin(30 + β) =
= sin30cosβ + cos30sinβ =
= 1/2 × 3/5 + √3/2 × 4/5 =
= 3/10 + 2√3/5
sin(60 - β) =
= sin60cosβ - cos60sinβ =
= √3/2 × 3/5 - 1/2 × 4/5 =
= 3√3/10 - 2/5