Question

Rozwiąż równanie 2cos²x + 5sinx - 4 = 0

Answer 1

2cos²x + 5sinx - 4 = 0
2(1 - sin²x) + 5sinx - 4 = 0
2 - 2sin²x +5 sinx - 4 =0
-2sin²x + 5sinx - 2 =0

niech sinx = t ∧ -1 ≤ t ≤ 1
-2t² + 5t - 2 = 0
Δ=25-16=9
t₁=(-5+3)/(-4)=0,5
t₂=(-5-3)/(-4)=2
więc sinx = t₁ = 0,5

x=π/6 +2kπ ∨ x=5π/6 + 2kπ, k∈C