SOLUTION: The equation tan x = 4 cos x has two roots in the interval -180 <= x => 180. These are denoted by A and B, where A > B. Express B in terms of A.

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Question 440735: The equation tan x = 4 cos x has two roots in the interval -180 <= x => 180. These are denoted by A and B, where A > B. Express B in terms of A.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
tan x = 4 cos x
sin/cos = 4cos
sin = 4cos^2
sin = 4(1-sin^2) = 4 - 4sin^2
4sin^2 + sin - 4 = 0
Sub x for sine:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B1x%2B-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%29%5E2-4%2A4%2A-4=65.

Discriminant d=65 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+65+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+65+%29%29%2F2%5C4+=+0.882782218537319
x%5B2%5D+=+%28-%281%29-sqrt%28+65+%29%29%2F2%5C4+=+-1.13278221853732

Quadratic expression 4x%5E2%2B1x%2B-4 can be factored:
4x%5E2%2B1x%2B-4+=+%28x-0.882782218537319%29%2A%28x--1.13278221853732%29
Again, the answer is: 0.882782218537319, -1.13278221853732. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B1%2Ax%2B-4+%29

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Disregard the -1.1... value
sin(x) =~ 0.8827822
x =~ 61.979º
x =~ 118.02º