Solve over the interval [0,2π) 2(cos^2)x+cosx=0

Solve over the interval [0,2π) 2(cos^2)x+cosx=0

Question
Functions
asked 2021-02-05
Solve over the interval PSK[0,2π) 2(cos^2)x+cosx=0ZSK

Answers (1)

2021-02-06
The terms of \(\displaystyle{2}{\left({\cos}^{{2}}\right)}{x}+{\cos{{x}}}={0}\) have a common factor of \(\displaystyle{\cos{{x}}}\). Factoring out \(\displaystyle{\cos{{x}}}{t}{h}{e}{n}{g}{i}{v}{e}{s}{P}{S}{K}{\cos{{x}}}{\left({2}{\cos{{x}}}+{1}\right)}={0}\).
The Zero Product Property states that if ab=0, then a=0 or b=0. Therefore, if cosx(2cosx+1)=0ZSK, then \(\displaystyle{\cos{{x}}}={0}\) \ or \ \(\displaystyle{2}{\cos{{x}}}+{1}={0}\).
From the unit circle, \(\displaystyle{\cos{{x}}}={0}\) when \(\displaystyle{x}=
0

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