Question

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

Answer 1

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