SOLUTION: Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a graphing utility to approximate the angle x (Round each answer to four decimal places) 12

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Question 847344: Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a graphing utility to approximate the angle x (Round each answer to four decimal places)
12 sin^2 x − 17 sin x + 6 = 0
5 tan^2 x + 8 tan x − 4 = 0
tan^2 x + 4 tan x + 1 = 0
4 cos^2 x − 4 cos x − 1 = 0
4 tan^2 x + 21 tan x − 49 = 0
tan^2 x + 5 tan x + 2 = 0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a graphing utility to approximate the angle x (Round each answer to four decimal places)
12sin^2(x) - 17sin(x) + 6 = 0 ************ don't put spaces after coefficients.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 12x%5E2%2B-17x%2B6+=+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=%28-17%29%5E2-4%2A12%2A6=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--17%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-17%29%2Bsqrt%28+1+%29%29%2F2%5C12+=+0.75
x%5B2%5D+=+%28-%28-17%29-sqrt%28+1+%29%29%2F2%5C12+=+0.666666666666667

Quadratic expression 12x%5E2%2B-17x%2B6 can be factored:
12x%5E2%2B-17x%2B6+=+%28x-0.75%29%2A%28x-0.666666666666667%29
Again, the answer is: 0.75, 0.666666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B-17%2Ax%2B6+%29

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sin(x) = 3/4
Use a calculator to find x
You can't get 4 decimal places on a graph.
----------------------
sin(x) = 2/3
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do the others the same way.
5 tan^2 x + 8 tan x − 4 = 0
tan^2 x + 4 tan x + 1 = 0
4 cos^2 x − 4 cos x − 1 = 0
4 tan^2 x + 21 tan x − 49 = 0
tan^2 x + 5 tan x + 2 = 0