+130555 3sin (2theta) +1=0 subtract 1 from both sides
3sin(2Θ) = -1 divide by 3 on both sides
sin(2Θ) = -1/3
sin(Θ) = -1/3 at about -19.5° = 199.5°, 340.5°, 559.5° and at 700.5°.....dividing all by 2, we have....
Θ = about 99.8°, 170.3°, 279.8° and 350.3°
Here's a graph......https://www.desmos.com/calculator/78mdpgxfc7
+130555 Here's a little more about Melody's answer......
This is a hyperbola....the "minus" sign between the first two terms tells us this.. it also opens "upward and downward"........this is easy to spot because the variable that comes first - in this case, "y' - will tell us which axis the hyperbola intersects
As in all conic forms, the center is found at (1/√2, -3/√2)
The transverse axis is given by the equation ....x = 1/√2.......the focal points lie on this line and are located at (1/√2, -3/√2 ± √[a2 + b2]) = (1/√2, -3/√2 ± 10√2)
And the asymptotes are given by .... y = ±(a/b)(x - h) + k =
±(10/10)(x - 1/√2) - 3/√2 = ± (x - 1/√2) - 3/√2
Here's a graph that puts all this together.......https://www.desmos.com/calculator/pskcr0hrmy
Here's a good website covering the basics of the hyperbola.....http://www.purplemath.com/modules/hyperbola.htm
