SOLUTION: What is the minimum value of 4 sec^2 theta + 9 cosec^2 theta ? we know the minim value of sec^2 theta is 1. but don't know how to covert the equation completely in to terms of s

Algebra ->  Trigonometry-basics -> SOLUTION: What is the minimum value of 4 sec^2 theta + 9 cosec^2 theta ? we know the minim value of sec^2 theta is 1. but don't know how to covert the equation completely in to terms of s      Log On


   

Question 636700: What is the minimum value of 4 sec^2 theta + 9 cosec^2 theta ?
we know the minim value of sec^2 theta is 1. but don't know how to covert the equation completely in to terms of sec^2 theta.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What is the minimum value of 4 sec^2 theta + 9 cosec^2 theta ?
we know the minim value of sec^2 theta is 1. but don't know how to covert the equation completely in to terms of sec^2 theta.
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z = 4sec^2 + 9csc^2
dz/dx = 4*2*sec*sec*tan + 9*2*csc*(-csc*cot)
dz/dx = 8sec^2tan - 18csc^2cot = 0
8sin/cos^3 - 18cos/sin^3 = 0
8sin^4 - 18cos^4 = 0
4sin^4 = 9cos^4
2sin^2 = 3cos^2
tan^2 = -sqrt(3/2),sqrt(3/2)
tan%28x%29+=+root%284%2C1.5%29
Find x, then sub into z = 4sec^2 + 9csc^2 to find the minimum, 25