SOLUTION: Approximate to the nearest degree, the solutions of the equation in the interval [0, 360) sin^2(t)-5sin(t)+1=0. I do know that there will be two answers, I'm just not sure wh

Algebra ->  Trigonometry-basics -> SOLUTION: Approximate to the nearest degree, the solutions of the equation in the interval [0, 360) sin^2(t)-5sin(t)+1=0. I do know that there will be two answers, I'm just not sure wh      Log On


   

Question 467088: Approximate to the nearest degree, the solutions of the equation in the interval [0, 360)
sin^2(t)-5sin(t)+1=0.
I do know that there will be two answers, I'm just not sure what they are;-).
Thanks you in advance!!!!!!!!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Sub x for sin(t)
x%5E2+-+5x+%2B+1+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-5x%2B1+=+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=%28-5%29%5E2-4%2A1%2A1=21.

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

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+21+%29%29%2F2%5C1+=+4.79128784747792
x%5B2%5D+=+%28-%28-5%29-sqrt%28+21+%29%29%2F2%5C1+=+0.20871215252208

Quadratic expression 1x%5E2%2B-5x%2B1 can be factored:
1x%5E2%2B-5x%2B1+=+%28x-4.79128784747792%29%2A%28x-0.20871215252208%29
Again, the answer is: 4.79128784747792, 0.20871215252208. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B1+%29

Ignore the answer that's >1.
sin(t) =~ 0.208712
t = 12 degs
t = 168 degs