Answer:
x = (1 + 4n)π/2, where n = any integer
Step-by-step explanation:
7sin²x -14sinx + 2 = -5
Add 5 to each side: 7sin²x -14sinx + 7 = 0
Divide each side by 7: sin²x - 2sinx + 1 = 0
Factor the perfect square: (sinx -1)(sinx -1) = 0
Solve: sinx - 1 = 0
Add 1 to each side: sin x = 1
Take the arcsin of each side: x = π/2
However, this is only one solution.
sinx is a periodic function, and π/2 ± 2πn is also a solution.
π/2 ± 2πn = π/2(1 ± 4n)
We can write the general solution as x = (4n + 1)π/2 where n = any integer.
