Question

list all x intercepts for y= -cos(1/2x + 1/5 pi) on the interval [-2/5pi,4pi]

Answer 1

The x intercepts are where y=0 So you get 0=-cos(1/2x+pi/5) Well, where is cos(x) zero? pi/2,3pi/2,5pi/2, etc. or (2n+1)pi/2 So set 1/2x+pi/5=pi/2 You get:
1/2x=3pi/10
x=6pi/10=3pi/5
But also, 8pi/5.
So just go for all "pi/2"'s in the domain. Which is pi/2, 3pi/2,5pi/2,7pi/2. There is probably a pattern but i don't remember it :/

Answer 2

Actually, even better.Do:
\[\frac{1}{2}x+\frac{\pi}{5}=\frac{\pi}{2}+n \pi\]. Since that will let you solve for any n multiple. Then you get (3/5)pi+2npi. So just add 2pi to get all your solutions.

Answer 3

That make sense/help?