Question

Solve 8 sin2x 10sin x =0 for all solutions.

Answer 1

To solve the equation 8 sin^2(x) + 10 sin(x) = 0, we can factor out sin(x) from the equation and set each factor equal to zero. The solutions are x = 0 and x = pi.

Step-by-step explanation:

To solve the equation 8 sin^2(x) + 10 sin(x) = 0, we can factor out sin(x) from the equation:

sin(x)(8 sin(x) + 10) = 0

Now we can set each factor equal to zero and solve for x:

sin(x) = 0 or 8 sin(x) + 10 = 0

For sin(x) = 0, the solutions are x = 0 and x = pi. For 8 sin(x) + 10 = 0, we can solve for sin(x) by subtracting 10 and dividing by 8, giving sin(x) = -10/8 = -5/4. However, this is not a valid solution since the range of sine function is -1 to 1. Therefore, the only solutions to the equation are x = 0 and x = pi.