General Solutions Part II

Hi, Patrick here with some General Solutions info,

In addition to what Christian posted last time about General Solutions, we now have a different equation to work with.
sin3Θ = -√2/2
you solve this equation the exact same way you would solve any other general solution equations.

BUT before you give your final answer you need to divide both sides by the co-efficient that is beside the theta. Example: (3Θ)/3 = (5π/4 + 2kπ)/3
                       Θ = 5π/12 +2/3kπ

In another solution you could also be given:
secΘ/2+2=0
To solve this equation you just need to multiply the final steps instead of dividing.


For equations like these that give you an interval, make sure your answer doesnt go over it.
*Be sure to double check your answers with the interval!*
Solve for Θ over the interval 0 ≤ Θ ≤ 2π

sinΘ/2 = 0

Θ/2 = (0, π, 2π)²
Θ= 0, 2π, 4π  (4π falls outside the interval given, so it is not included in the final answer, cross it out after you have double checked)

Now probably the one that is going to drive most people crazy:

sec3Θ = √2
The 3 determines how many revolutions you will have to provide in your final answer.
*Only when the interval is specified do you do the revolutions.*