How do I do this fminsearch problem?

2018 10 22
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更新时间：2018 10 22
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x^2 + 2*cos(θ) + y = α
x^2 −(3/2)*sin(θ) − y = 2.
Use the fminsearch function and the above system to find the minimum solution for α. Use initial guesses for x = 0 and y = 0. (Hint: This means solve the above equations by eliminating θ)

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回答（1 个）

Walter Roberson
Walter Roberson 2018-10-22

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If
x^2 −(3/2)*sin(θ) − y = 2
then
x^2 −(3/2)*sin(θ) − y - x^2 + y = 2 - x^2 + y
so
-(3/2)*sin(theta) = 2 - x^2 + y
so
sin(theta) = 2/3 * (-2 + x^2 - y)
and then
theta = arcsine(2/3 * (x^2 - y - 2))
Substitute that into the first equation
x^2 + 2*cos( asin(2/3 * (x^2 - y - 2))) + y = alpha
and to minimize alpha, minimize the left hand side of that.

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