How many solutions are there for the system of equations y = sin^2x – 2^(1/2) sinx – 1 and y = x – 3 on the interval [0, 2π)?

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1 Answer
Douglas K.
Mar 30, 2018

There is one solution.

Explanation:

One can obtain an equation in x by setting the right sides of the two equations equal:

#x - 3 = sin^2(x)-sqrt2sin(x)-1#

But this does no good because the equation cannot be solved using algebraic means.

I used a free online graphing calculator, Desmos, and observed that the graphs cross at only 1 point:

www.desmos.com/calculator

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