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

- cos ( 1/2 x + 1/5 π ) = 0 ( and because if cos α = 0, α= π/2 + k π, k ∈ Z )
1/2 x + π/5 = π/2 + k π,    k ∈ Z
1/2 x = π/2 - π/5 + k π  / * 2
x = π - 2π/5 + 2 k π
x = 3/5 π + 2 k π = 0.6 π + 2 k π
Answer:
If k = 0:  x 1 = 0.6 π = 3π/5
k = 1 : x 2 = 2.6 π = 13π/5