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Please help! solve: 4sin³x+2sin²x2sinx1=0 for 0° ≤ x ≤ 360°
 6 months ago
 6 months ago
Please help! solve: 4sin³x+2sin²x2sinx1=0 for 0° ≤ x ≤ 360°
 6 months ago
 6 months ago

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jdoe0001Best ResponseYou've already chosen the best response.1
can you take common factor on the lefthand side?
 6 months ago

baseballguy1322Best ResponseYou've already chosen the best response.0
common factor would be sin(x) right?
 6 months ago

jdoe0001Best ResponseYou've already chosen the best response.1
... h... actually... after getting rid of the 1, yes
 6 months ago

baseballguy1322Best ResponseYou've already chosen the best response.0
You add 1 to the right side but what would the left hand side look like after you simplify the gcf
 6 months ago

jdoe0001Best ResponseYou've already chosen the best response.1
\(\bf 4sin^3(x)+2sin^2(x)2sin(x)1=0\\ \quad \\ 4sin^3(x)+2sin^2(x)2sin(x)=1\\ \quad \\ 2sin(x)\quad [2sin^2(x)+sin(x)1] = 1\)
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
So are you looking to solve 4u^3+2u^22u1=0 Did you try to find the possible 0's?
 6 months ago

jdoe0001Best ResponseYou've already chosen the best response.1
yea... I think so @myininaya is correct.. you may have to factor it with the 0 on the righthand side
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
or you could factor by grouping :) much simpler
 6 months ago

baseballguy1322Best ResponseYou've already chosen the best response.0
Yes I am trying to solve for the possible solutions in degrees. How would you factor by grouping?
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
\[(4\sin^3(x)+2\sin^2(x))+(2\sin(x)1)=0\]
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
Look at those first two terms. They have common factor. Look at the last terms. Factor out 1.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
Or you can look at it in terms of u instead of sin at first. Your choice.
 6 months ago

baseballguy1322Best ResponseYou've already chosen the best response.0
would it be 2sin^3(x) +sin(x)) + (2sin(x))=0 ?
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
\[(4u^3+2u^2)+(2u1)=0\]
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
What does 4u^3 and 2u^2 have in common?
 6 months ago

baseballguy1322Best ResponseYou've already chosen the best response.0
2u^2? or just u^2?
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
The gcf would be 2u^2 So we have \[2u^2(2u+1)+(2u1)=0\] Those last two terms, you can factor out 1.
 6 months ago

baseballguy1322Best ResponseYou've already chosen the best response.0
2u^2(2u+1) + ( 2sin) = 0
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
So (2sin(x)1)=(2sin(x)+1)
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
\[2u^2(2u+1)1(2u+1)=0\] Now you have two terms. (2u+1) is a factor of both of those terms. Do you think you can completely factor the left hand side now.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
Don't forget about the (2u+1) So to factor \[2u^2(2u+1)1(2u+1) \text{ we find what both of our terms have in common } \] The (2u+1) So we factor the (2u+1) out giving us \[(2u+1)(2u^21)=0\] Set both factors equal to 0. Don't forget u is sin(x).
 6 months ago

baseballguy1322Best ResponseYou've already chosen the best response.0
Oh yeah that's right, I haven't done factoring in awhile. what would be the next step after this one?
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
Setting both factors equal to 0.
 6 months ago

baseballguy1322Best ResponseYou've already chosen the best response.0
sin x +1 = 0 sin x = 1 and sin^2x1=0 sin^2x = 1
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
Your 2's are disappearing?
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
\[2u+1=0 \text{ or } 2u^21=0\] \[2u=1 \text{ or } 2u^2=1\] \[u=\frac{1}{2} \text{ or } u^2=\frac{1}{2}\]
 6 months ago

baseballguy1322Best ResponseYou've already chosen the best response.0
How would you convert that to degrees for the final answer?
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
sin(x)=1/2 Did I just show you the unit circle?
 6 months ago

baseballguy1322Best ResponseYou've already chosen the best response.0
is it 210 and 330 degrees?
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
You also need to solve sin^2(x)=1/2 Take the square root of both sides \[\sin(x)=\pm \sqrt{ \frac{1}{2} }\] Don't forget to solve these two as well. And yes those are the solutions to sin(x)=1/2
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
Now for this one, it maybe easy for you to rationalize the denominator first before looking on the unit circle.
 6 months ago

baseballguy1322Best ResponseYou've already chosen the best response.0
so the four answers would be 30, 150, 210, and 330 degrees?
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
\[\sin(x)=\frac{\sqrt{2}}{2} \text{ or } \sin(x)=\frac{\sqrt{2}}{2}\] I don't think you solved these correctly.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
You solved sin(x)=1/2 correctly. So part of your answer is 210 and 330 degrees.
 6 months ago

baseballguy1322Best ResponseYou've already chosen the best response.0
okay thanks for the help
 6 months ago

myininayaBest ResponseYou've already chosen the best response.2
Np. You got it from here?
 6 months ago

baseballguy1322Best ResponseYou've already chosen the best response.0
yeah i got it.
 6 months ago
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