Use the inverse functions to find all solutions in the interval $[0, 2π)$ $3cos^2(x) + 5cos(x) = 0$ ?

Question

1072 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-25T11:02:47

$pi/2$ and $(3pi)/2$

We can factorise this equation to get:
$cos(x)(3cos(x)+5)=0$

$cosx=0 or cosx=-5/3$

$x=cos^-1(0)=pi/2,2pi-pi/2;pi/2,(3pi)/2$
or
$x=cos^-1(-5/3)="undefined"$ , $abs(cos^-1(x))<=1$

So, the only solutions are $pi/2$ and $(3pi)/2$

Use the inverse functions to find all solutions in the interval [0, 2π)[0, 2π) 3cos^2(x) + 5cos(x) = 03cos^2(x) + 5cos(x) = 0?