To make the calculations easier, for now, replace "sin(2θ)" with x:
Then we have: x2 - 5x - 1 = 0
Using the quadratic formula: x = [5 + √(25 + 4)] / 2 ≈ 5.1926
or x = [5 - √(25 + 4)] / 2 ≈ -0.19258
Since x = sin(2θ): sin(2θ) = 5.1926 or sin(2θ) = -0.19258
---> 2θ = sin-1(5.1928) or 2θ = sin-1(-0.19528)
---> θ = sin-1(5.1928) / 2 or θ = sin-1(-0.19528) / 2
Since sin does not have a value larger than 1, θ = sin-1(5.1928) / 2 is an impossibility.
For θ = sin-1(-0.19528) / 2,
θ equals either 275.55° or 354.4° (and all multiples of 180°, larger and smaller).
To make the calculations easier, for now, replace "sin(2θ)" with x:
Then we have: x2 - 5x - 1 = 0
Using the quadratic formula: x = [5 + √(25 + 4)] / 2 ≈ 5.1926
or x = [5 - √(25 + 4)] / 2 ≈ -0.19258
Since x = sin(2θ): sin(2θ) = 5.1926 or sin(2θ) = -0.19258
---> 2θ = sin-1(5.1928) or 2θ = sin-1(-0.19528)
---> θ = sin-1(5.1928) / 2 or θ = sin-1(-0.19528) / 2
Since sin does not have a value larger than 1, θ = sin-1(5.1928) / 2 is an impossibility.
For θ = sin-1(-0.19528) / 2,
θ equals either 275.55° or 354.4° (and all multiples of 180°, larger and smaller).