I'm not asking how to do a problem, just if I did it right.
Ok, it may be a long one:
(for the purpose of writing on the computer, # is gonna be pie (3.14), and it would be like your typing it into a calculator since there's only so much you can type)
Original question: "Find all solutions in the interval [0,2#): 2sin^2(x/4)-3cos(x/4)=0"
Ok, this is what I got:
THIS IS WHAT I MEANT by ALL of the sin^2(u) (in the pictures case x)
2sin^2(x/4)-3cos(x/4)=0
Let u=x/4
2sin^2(u)-3cos(u)
2(1-cos^2(u))-3cos(u)
2-2cos^2(u)-3cosu
(-1)-2cos^2(u)-3cos(u)+2
2cos^2(u)+3cos(u)-2
Factored:
(2cos(u)-1)(cos(u)+2)
Solving for each one:
2cos(u)-1=0
cos(u)=1/2
arccos(1/2)=u
u=#/3, 5#/3
And the other:
cosu+2=0
cosu=-2
arccos(-2)=u
Doesn't work so I reject this answer?
Anyway, so (substitute back in):
x/4=#/3 , x/4=5#/3
so:
x=4#/3 , x=20#/3
I'm only solving for [0,2#) so:
{x=4#/3}
And that would be my final answer?
Just wondering. I think I might have done something wrong since only 1 out of the 4 possible answers would be the correct one.
Edit:
Fixed stupid u^2
Edit2:
Fixed ^2 AGAIN.
Ok, it may be a long one:
(for the purpose of writing on the computer, # is gonna be pie (3.14), and it would be like your typing it into a calculator since there's only so much you can type)
Original question: "Find all solutions in the interval [0,2#): 2sin^2(x/4)-3cos(x/4)=0"
Ok, this is what I got:
THIS IS WHAT I MEANT by ALL of the sin^2(u) (in the pictures case x)
2sin^2(x/4)-3cos(x/4)=0
Let u=x/4
2sin^2(u)-3cos(u)
2(1-cos^2(u))-3cos(u)
2-2cos^2(u)-3cosu
(-1)-2cos^2(u)-3cos(u)+2
2cos^2(u)+3cos(u)-2
Factored:
(2cos(u)-1)(cos(u)+2)
Solving for each one:
2cos(u)-1=0
cos(u)=1/2
arccos(1/2)=u
u=#/3, 5#/3
And the other:
cosu+2=0
cosu=-2
arccos(-2)=u
Doesn't work so I reject this answer?
Anyway, so (substitute back in):
x/4=#/3 , x/4=5#/3
so:
x=4#/3 , x=20#/3
I'm only solving for [0,2#) so:
{x=4#/3}
And that would be my final answer?
Just wondering. I think I might have done something wrong since only 1 out of the 4 possible answers would be the correct one.
Edit:
Fixed stupid u^2
Edit2:
Fixed ^2 AGAIN.