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.

Algebra ->  Trigonometry-basics -> 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.      Log On


   

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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 20x%5E2%2B-21x%2B4+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-21%29%5E2-4%2A20%2A4=121.

Discriminant d=121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--21%2B-sqrt%28+121+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-21%29%2Bsqrt%28+121+%29%29%2F2%5C20+=+0.8
x%5B2%5D+=+%28-%28-21%29-sqrt%28+121+%29%29%2F2%5C20+=+0.25

Quadratic expression 20x%5E2%2B-21x%2B4 can be factored:
20x%5E2%2B-21x%2B4+=+%28x-0.8%29%2A%28x-0.25%29
Again, the answer is: 0.8, 0.25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+20%2Ax%5E2%2B-21%2Ax%2B4+%29

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sin(x) = 0.8
x = 0.9273
x = pi - 0.9273 = 2.2134
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sin(x) = 0.25
x = 0.2527
x = pi - 0.2527 = 2.8889