Solve trigonometric equation: sin x + sin 2x + sin 3x = 0. Math Olympiad Algebra Problem.

How to solve trigonometric equation: sin x + sin 2x + sin 3x = 0. Challenging Algebra Problem. Math Olympiad Algebra Problem. Step-by-step tutorial by Fun with Maths.

[MichaelRothwell]

The solution in the video is exactly the same as solution I came up with, using the sum to product formula. However, there is an error in the solution in the video in the step cos x=-1/2 ⇒x=arccos(-1/2), since arccos(-1/2) has the single value 2π/3, whilst the equation cos x=-1/2 has infinitely many solutions. Note that arccos is a function that by definition is the inverse of the function cos restricted to the domain [0, π], where it is one-to-one and has the same range as the full cos function. This means that arccos a is the unique solution in x to the equation cos x=a in the interval [0, π], the so called principal value.

[jeanlismonde]

il existe triple infinité de solutions : x = pi/4 + k.pi, x = 2pi/3 + 2kpi et x = 4pi/3 + 2kpi
pour cela il suffit de factoriser ta somme trigo sachant que sinx +sin(3x) = 2sin2x.cosx soit
sin(2x)(1+2cosx) = 0 et donc les trois solutions indiquées

[JSSTyger]

Here are the solution sets. Using k as the set of all integers,
x = kπ, x = π/2+kπ, x = 2π/3+2kπ, and x = 4π/3+2kπ. The first two sets, however, are both part of the same set x = kπ/2.

[Nikioko]

sin 0 = 0, therefore x = 0. ;-)
But sin 2π = 0 as well, so x can be any multiple of 2π.

[yalc-]

Why is this in my recommendations? 😂😂 Bro I literally just had to take 7 whole seconds to figure out what 8+8 was

I'm not in elementary school fyi


Ask a English or history question and I'm your man but I can't do any form of advanced math 😅