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 :/
- 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
