sinL=0,6 sinB=0,8 L+B+Y=180* Oblicz: sinY=?

sinL = 3/5 => L∈(0; 180) sinB = 4/5 => B∈(0; 180) L+B+Y = 180 => Y = 180-(L+B) sinY = sin(180-(L+B)) = sin(L+B) = sinL cosB + cosL sinB cos²L = 1 - sin²L cos²L = 1 - 9/25 = 16/25 cosL = 4/5 ∨ cosL = -4/5 cos²B = 1 - sin²B cos²B = 1 - 16/25 = 9/25 cosB = 3/5 ∨ cosB = -3/5 sinY = 3/5 * 3/5 + 4/5 * 4/5 = 9/25 + 16/25 = 1 ∨ sinY = 9/25 - 16/25 = -7/25 ∨ sinY = -9/25 + 16/25 = 7/25 ∨ sinY = -9/25 - 16/25 = -1 odp: sinY = 1 ∨ sinY = -1 ∨ sinY = 7/25 ∨ sinY = -7/25