To solve the equation 6sin^2(x) + sin(x) = 2, follow these steps:
Let sin(x) = y. The equation becomes 6y^2 + y = 2.Rearrange the equation to get 6y^2 + y - 2 = 0.Factor the quadratic equation: (3y - 2)(2y + 1) = 0.Set each factor to zero and solve for y: 3y - 2 = 0 or 2y + 1 = 0 y = 2/3 or y = -1/2Substitute back sin(x) for y: sin(x) = 2/3 or sin(x) = -1/2Solve for x: x = sin^(-1)(2/3) or x = sin^(-1)(-1/2)
Thus, the solutions to the equation are: x = sin^(-1)(2/3) + 2πn, where n is an integer x = sin^(-1)(-1/2) + 2πn, where n is an integer.
To solve the equation 6sin^2(x) + sin(x) = 2, follow these steps:
Let sin(x) = y. The equation becomes 6y^2 + y = 2.Rearrange the equation to get 6y^2 + y - 2 = 0.Factor the quadratic equation: (3y - 2)(2y + 1) = 0.Set each factor to zero and solve for y:3y - 2 = 0 or 2y + 1 = 0
y = 2/3 or y = -1/2Substitute back sin(x) for y:
sin(x) = 2/3 or sin(x) = -1/2Solve for x:
x = sin^(-1)(2/3) or x = sin^(-1)(-1/2)
Thus, the solutions to the equation are:
x = sin^(-1)(2/3) + 2πn, where n is an integer
x = sin^(-1)(-1/2) + 2πn, where n is an integer.