How To ACTUALLY Solve a Cubic Equation using Trigonometry

This is a really nice method for solving cubic equations with three real roots! The method involves using the triple angle formula for cosine or sine and then solving a related trigonometric equation: all fairly elementary methods.

Worked example: 8:45

[fredblogs]

You do not understand how long I've tried to find a video that explains this clearly! Thank you my good Sir!!

[StevenLitvintchouk]

I've used Cardano's Method, but this trig method I've never seen or heard of before. Thank you!

[TitoTheThird]

The well-known method to solve the quintic x^5+px+q=0 using elliptic functions (which are doubly-periodic) just generalizes the solution to the cubic x^3+px+q=0 using trigonometric functions (which are singly-periodic).

[mab]

Thank you bro. Best method so far to resolve such equations.

[dominicellis]

I used cardanos method to find an explicit expression for cos(theta/3) to find the value of cos or sin at pi/9 and pi/18 but this is so brilliant.

[deborahkeesee]

I know just enough math to be very impressed with this guy, but that's about all.

[LydellAaron]

Fantastic video showing how to use trigonometry to solve polynomial equations. Great topic.

[AndrewTota]

THAT IS THE CUTEST MATH TEACHER I HAVE EVER SEEN IN MY LIFE

[barryzeeberg]

And the final answer comes out in terms of closed form functions, which might just give some insight into the physical meaning of the solution in some lucky cases. Would it be possible to alternatively use the Euler formula to solve this using the complex plane?

[iconic]

The last thing I expected to see when clicking on this vid, was a super jacked dude.

[MsDavo]

This was just fucking amazing and so much clarity here!Love your lecturing style bro!

[charlesquinn]

I wonder if you could do this for quartics 🤔

[aubertducharmont]

Wow, just wow. I have never before seen anything like that. You explained everything so nicely. Btw, there is another way to solve cubic equations, and it is called cardano's method. I think you would find it pretty interesting.

[giuseppecolia]

I didn't understand how he has found cos^3θ-3/4cosθ-1/4cos(3θ). Can anyone explain it?

[bobbyheffley]

If a cubic equation has three unequal real roots, trigonometric solutions avoid the irreducible case in the radical forms.

[reubenmanzo]

How come y has to be positive?
Also, why specifically cos? Does sin work?

[mathisnotforthefaintofheart]

Where would this method "break down" if the cubic only has one real root? I admit, I have not tried it out

[yapsiauwsoengie]

Why this method won't work for:
X^3-3x^2-3x-1=0
By letting u=x-1
u^3-6u-6=0
The cos 3 theta value > than 1

[TruthOfZ]

Why? Is it hard to solve it the algebraic way? like quadratic equations? why do it the hard way?

[Daisy_s_pace]

Indian students also learning from uhh😊