A Cool Trigonometric Equation

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[@kassuskassus6263]

Yessss...for the second method !

[@MrGeorge1896]

Second method but different: sin² (x) cos² (x) = 3/16 and with sin(x) cos(x) = 1/2 sin(2x): sin² (2x) = 3 / 4 sin(2x) = ± √3 / 2 so x = n π ± π/3 or x = n π ± π/6 with n ∈ ℤ.

[@BurningShipFractal]

I also did with that method

[@tygrataps]

I explored putting all of the answers together and came up with an odd pattern, 1/6, 2/6, 4/6, 5/6, 7/6, etc. Basically, every 1/6 that isn't divisible by 1/2? Could that even be more clearly written?

[@udic01]

7:44 you have an error. The factorization should be (4y-3)*(4y-1). The 4y-1=0 gives you the pi/6 and 5pi/6

[@DonEnsley-yi2ql]

x = tan ⁻¹[(2 ± i√19)/√23] + kπ, k an integer