SOLUTION: I am having troubles with this equations any ideas. Your time is greatly appreciated. Find the smallest positive number such that sin^2(t) + 1.8sin(t)-0.4=0

Algebra ->  Trigonometry-basics -> SOLUTION: I am having troubles with this equations any ideas. Your time is greatly appreciated. Find the smallest positive number such that sin^2(t) + 1.8sin(t)-0.4=0       Log On


   

Question 669344: I am having troubles with this equations any ideas. Your time is greatly appreciated. Find the smallest positive number such that sin^2(t) + 1.8sin(t)-0.4=0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the smallest positive number such that sin^2(t) + 1.8sin(t)-0.4=0
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Sub x or sin(t)
x%5E2+%2B+1.8x+-+0.4+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1.8x%2B-0.4+=+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=%281.8%29%5E2-4%2A1%2A-0.4=4.84.

Discriminant d=4.84 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1.8%2B-sqrt%28+4.84+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281.8%29%2Bsqrt%28+4.84+%29%29%2F2%5C1+=+0.2
x%5B2%5D+=+%28-%281.8%29-sqrt%28+4.84+%29%29%2F2%5C1+=+-2

Quadratic expression 1x%5E2%2B1.8x%2B-0.4 can be factored:
1x%5E2%2B1.8x%2B-0.4+=+%28x-0.2%29%2A%28x--2%29
Again, the answer is: 0.2, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1.8%2Ax%2B-0.4+%29

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sin(t) = -2 Ignore, tho it has a complex number solution.
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sin(t) = 0.2
t = asin(0.2), you pick degrees or radians