Question

Solve the following equation, giving the exact solutions which lie in [0, 2π).

cos^3(x) = −cos(x)

Answer 1

start with
\[\cos^3(x)+\cos(x)=0\] then factor as
\[\cos(x)(\cos^2(x)+1)=0\]

Answer 2

since \(\cos^2(x)+1\) can never be zero, solve \(\cos(x)=0\) and you are done

Answer 3

Should that be pi/2 and 3pi/2 ?

Answer 4

why cos^2(x)+1 can never be zero anyway?

Answer 5

@Rahaf, \(\cos^2x\ge0,\) so if you add one to both sides, you have \(\cos^2x+1\ge1\).

Answer 6

oh ok thanks @SithsAndGiggles