SOLUTION: secA+tanA= 4, then find sinA

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Question 623387: secA+tanA= 4, then find sinA
Answer by Alan3354(69443) About Me  (Show Source):
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secA+tanA= 4, then find sinA
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secA+tanA= 4
1/cos + sin/cos = 4
sin%28A%29+%2B+1+=+4cos%28A%29+=+4%2Asqrt%281+-+sin%5E2%28A%29%29
Square both sides
sin^2 + 2sin + 1 = 16 - 16sin^2
17sin^2 + 2sin - 15 = 0
Sub x for sin(A)
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 17x%5E2%2B2x%2B-15+=+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=%282%29%5E2-4%2A17%2A-15=1024.

Discriminant d=1024 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+1024+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+1024+%29%29%2F2%5C17+=+0.882352941176471
x%5B2%5D+=+%28-%282%29-sqrt%28+1024+%29%29%2F2%5C17+=+-1

Quadratic expression 17x%5E2%2B2x%2B-15 can be factored:
17x%5E2%2B2x%2B-15+=+%28x-0.882352941176471%29%2A%28x--1%29
Again, the answer is: 0.882352941176471, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+17%2Ax%5E2%2B2%2Ax%2B-15+%29

sin = -1
The -1 solution can't be used - the secant is undefined.
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sin =~ 0.882353