Find all solutions to this equation
2sin²x + 3sinx + 1 = 0
let a = sin x
=> 2a^2 + 3x + 1 = 0
=> (a + 1)(2a + 1) = 0
=> a = -1 or a = -1/2
sin x = -1 or sin x = -1/2
Now it's damn easy. You can solve for x on your own.
This is a quadratic in sin(x) then
(2sin(x) + 1)(sin(x + 1)=0
sin(x) = -1/2 or sin(x) = -1
x = (-1)^k Arcsin(-1/2) +kπ or x = (-1)^k Arcsin(-1) +kπ where k any integer
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Verified answer
let a = sin x
=> 2a^2 + 3x + 1 = 0
=> (a + 1)(2a + 1) = 0
=> a = -1 or a = -1/2
sin x = -1 or sin x = -1/2
Now it's damn easy. You can solve for x on your own.
This is a quadratic in sin(x) then
2sin²x + 3sinx + 1 = 0
(2sin(x) + 1)(sin(x + 1)=0
sin(x) = -1/2 or sin(x) = -1
x = (-1)^k Arcsin(-1/2) +kπ or x = (-1)^k Arcsin(-1) +kπ where k any integer