Find the general solution to the following equation. Give your answers as a number plus a multiple of π(don't approximate).sec^2(u)=2+sec(u)?
- Iggy RockoLv 79 months ago
sec^2u = 2 + secu
sec^2u - secu - 2 = 0
(secu - 2)(secu + 1) = 0
secu = 2 or secu = -1
u = pi/3 + 2npi or u = 5pi/3 + 2npi or u = pi + 2npi for all integers, n
- ?Lv 79 months ago
Let s = sec(u). Rewrite as s²-s-2=0. Use the quadratic eqs or better yet, Factoring gives (s-2)(s+1)=0.
Thus s = [left for you].
Do that & we will take it from there if need be.
Ok, to your comment. The π/3 & 5π/3 are the primary solutions. They want ALL the solutions. That's why they asked you to write the answer with a free parameter like n.
The primary answers + 2πn ( and +2πm) are all the solutions.
Don't forget to vote BA !