SOLUTION: Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a graphing utility to approximate the angle x. (Enter your answers as a comma-separated list.

Question 787552: Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a graphing utility to approximate the angle x. (Enter your answers as a comma-separated list. Round each answer to four decimal places.)
20 sin2 x − 21 sin x + 4 = 0
I get these answers -> x =0.2527,0.9273
But the EX has 4 solutions and I don't know how to get the last 2???????

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
20 sin^2(x) - 21 sin(x) + 4 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=121 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.8, 0.25. Here's your graph:

===============
sin(x) = 0.8
x = 0.9273
x = pi - 0.9273 = 2.2134
----------
sin(x) = 0.25
x = 0.2527
x = pi - 0.2527 = 2.8889
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SOLUTION: Use the Quadratic Formula to solve the equation in the interval [0, 2&#960;). Then use a graphing utility to approximate the angle x. (Enter your answers as a comma-separated list.

SOLUTION: Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a graphing utility to approximate the angle x. (Enter your answers as a comma-separated list.