Asked by Megan
Find all x, -4pi < x < 6pi, such that [cos(x/3)]^4 + [sin(x/3)]^4 = 1
PLEASEEE HELPP! :(
PLEASEEE HELPP! :(
Answers
Answered by
Reiny
realizing that
m^4 + n^4 = (m^2 + n^2)^2 - 2(m^2)(n^2)
we can rewrite your equation as
((cos x/3)^2 + (sin x/3)^2)^2 - 2(sin x/3)^2 (cos x/3)^2 = 1
(1)^2 - 2(sin x/3)^2 (cos x/3)^2 = 1
(sin x/3)(cos x/3)=0
so x/3 = 0,pi,2pi or x = pi/2, 3pi/2
those are the answers from 0 to 2pi
now fill in the rest from -4pi to 6pi
m^4 + n^4 = (m^2 + n^2)^2 - 2(m^2)(n^2)
we can rewrite your equation as
((cos x/3)^2 + (sin x/3)^2)^2 - 2(sin x/3)^2 (cos x/3)^2 = 1
(1)^2 - 2(sin x/3)^2 (cos x/3)^2 = 1
(sin x/3)(cos x/3)=0
so x/3 = 0,pi,2pi or x = pi/2, 3pi/2
those are the answers from 0 to 2pi
now fill in the rest from -4pi to 6pi
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.