A Radically Golden Trigonometric Equation

[@lisaworldpeace]

We prefer radians. Degrees are for "normal people" 😂

[@SyberMath]

😁

[@coolbeans9992]

8:41 bless you

[@pizza8725]

The solution is sin^-1((sqrt(5l)-1)/2)+2pin and pi-sin^-1((sqrt(5)-1)/2))+2pin

[@trojanleo123]

Yayy for Geometry sometime soon! Wooohooo!

[@SyberMath]

😁😍

[@michaelanderson1457]

I love your videos!

[@SyberMath]

Glad to hear that! 😍

[@roberttelarket4934]

It’s not radical enough! Try cos x = -[(sin x)^(1/2)]cos 2x.

[@Wultuswuffel]

bless you

[@SyberMath]

likewise!

[@giuseppemalaguti435]

sinx=(√5-1)/2...x=38,17(no),x=180-38,17=141,827

[@scottleung9587]

Nice!

[@SyberMath]

Thanks!

[@holyshit922]

Proposition for video Calculate coefficients of Chebyshev polynomials with aplusbi and without With aplusbi (by comparing Re(exp(i*n*theta)) and binomial expansion for Re(exp(i*theta)^n)) Without aplusbi From cos(n*theta) = T_{n}(cos(theta)) derive recursive formula and solve it with exponential generating function Exponential generating function leads us to second order linear differential equation wich can be easily solved using Laplace transform To calculate nth derivative we can use general product rule (it looks like binomial expansion but istead of powers we have derivatives) We can also derive ordinary differential equation for Chebyshev polynomials and solve it by power series We will get recrusion for coefficients , we can solve it backwards , this recursion can be easily expressed as product After we find polynomial solution for Chebyshev ode we use condition y(1) = 1 to find formula for Chebyshev equation

[@JohnsonIdris112]

Geometry ❤

[@shlokthosar8094]

But sir you did squaring both sides .. So the no. Of roots got increased .. How can we filter those extra roots ? For ex:- √49=7 But ( +7)²=(-7)²=49 .. it means if we square roots get increased So how can we deal with it ?

[@shlokthosar8094]

I am not talking about particularly for this problem. But I am talking how to deal with it in general ?

[@SyberMath]

Either check the domain as you go forward or check the potential solutions at the end.

[@2012tulio]

x = 38 deg

[@SyberMath]

did you check?

[@MataniMath]

The approach value of x is x = 141.82º. If x = 38.17º, then the LHS = cos x > 0 and the RHS = - ✓(sin x) < 0.