Question

Find all solutions to the equation.

7 sin^2x - 14 sin x + 2 = -5

Answer 1

7 sin^2x - 14 sinx + 2 = -5

7 sin^2x - 14 sinx = -7

(÷ 7)

sin^2x - 2 sinx = -1

(sinx = y)

y^2 - 2y = -1

y^2 - 2y + 1 = 0

Δ = (-2)² - 4(1)(1)
Δ = 4 - 4 = 0

y' = y'' = (2+0)/2 = 2/2 = 1

sinx = y

sinx = 1

S { π/2 }