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

1 Answer
1s2s2p
May 25, 2018

#pi/2# and #(3pi)/2#

Explanation:

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#

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