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Ahmed Heakl
Oct 31, 2019

Trigonometric Equation Problem

in Math Problems

3sin(2x)-4cos(x)-5 What is the value of x?

11 comments
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Ian Fowler
Oct 31, 2019

You are missing an equal sign. Is it "= 0" ?

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Ahmed Heakl
Nov 12, 2019

Yes, It does equal to 0.

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Faizan Ahmed
Nov 12, 2019

11
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Ahmed Heakl
Nov 12, 2019

I want the solution algebrically not graphically

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Faizan Ahmed
Nov 12, 2019

We can clearly see the values of x from graph.

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Ian Fowler
Nov 12, 2019

I tried the standard approach: sin(2x) = 2sin(x)cos(x) followed by sin(x) = sqrt(1 - cos^2(x)) and ended up with a quartic in cos(x). It does not factor. As shown by Faizan above, graphical or iterative methods are you only hope.

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Faizan Ahmed
Nov 13, 2019

Quartic-eq-Newton-Raphson-Trig-eq
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Ian Fowler
Nov 13, 2019

There it is in all it's glory. Newton's Method has the advantage of converging quickly to the root. The only tricky part is finding a good starting value for x. For example, if there is a relative max or min inside the interval for the sign change then it can easily go south and blow up. Having said that, in today's world with graphing software readily available, it is easy and fool-proof to find an x0 that will quickly converge. Well done Faizan.


For those that are interested, the recursive formula in Newton's method finds the equation of the tangent at x = x0 and then finds the x-intercept of that tangent to produce x1 - a better approximation to the root. Then just rinse and repeat to produce x2, x3 ...


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