SOLUTION: secA+tanA= 4, then find sinA

Question 623387: secA+tanA= 4, then find sinA
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
secA+tanA= 4, then find sinA
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secA+tanA= 4
1/cos + sin/cos = 4

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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1024 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.882352941176471, -1. Here's your graph:

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