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baseballguy1322
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Please help! solve: 4sin³x+2sin²x2sinx1=0 for 0° ≤ x ≤ 360°
 10 months ago
 10 months ago
baseballguy1322 Group Title
Please help! solve: 4sin³x+2sin²x2sinx1=0 for 0° ≤ x ≤ 360°
 10 months ago
 10 months ago

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jdoe0001 Group TitleBest ResponseYou've already chosen the best response.1
can you take common factor on the lefthand side?
 10 months ago

baseballguy1322 Group TitleBest ResponseYou've already chosen the best response.0
common factor would be sin(x) right?
 10 months ago

jdoe0001 Group TitleBest ResponseYou've already chosen the best response.1
... h... actually... after getting rid of the 1, yes
 10 months ago

jdoe0001 Group TitleBest ResponseYou've already chosen the best response.1
well... 2sin(x)
 10 months ago

baseballguy1322 Group TitleBest 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
 10 months ago

jdoe0001 Group TitleBest ResponseYou've already chosen the best response.1
\(\bf 4sin^3(x)+2sin^2(x)2sin(x)1=0\\ \quad \\ 4sin^3(x)+2sin^2(x)2sin(x)=1\\ \quad \\ 2sin(x)\quad [2sin^2(x)+sin(x)1] = 1\)
 10 months ago

myininaya Group TitleBest 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?
 10 months ago

jdoe0001 Group TitleBest 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
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
or you could factor by grouping :) much simpler
 10 months ago

baseballguy1322 Group TitleBest 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?
 10 months ago

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

myininaya Group TitleBest 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.
 10 months ago

myininaya Group TitleBest 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.
 10 months ago

baseballguy1322 Group TitleBest ResponseYou've already chosen the best response.0
would it be 2sin^3(x) +sin(x)) + (2sin(x))=0 ?
 10 months ago

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

myininaya Group TitleBest ResponseYou've already chosen the best response.2
What does 4u^3 and 2u^2 have in common?
 10 months ago

baseballguy1322 Group TitleBest ResponseYou've already chosen the best response.0
2u^2? or just u^2?
 10 months ago

myininaya Group TitleBest 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.
 10 months ago

baseballguy1322 Group TitleBest ResponseYou've already chosen the best response.0
2u^2(2u+1) + ( 2sin) = 0
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
(2u1)=(2u+1)
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
So (2sin(x)1)=(2sin(x)+1)
 10 months ago

myininaya Group TitleBest 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.
 10 months ago

baseballguy1322 Group TitleBest ResponseYou've already chosen the best response.0
2u^21=0
 10 months ago

myininaya Group TitleBest 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).
 10 months ago

baseballguy1322 Group TitleBest 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?
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Setting both factors equal to 0.
 10 months ago

baseballguy1322 Group TitleBest ResponseYou've already chosen the best response.0
sin x +1 = 0 sin x = 1 and sin^2x1=0 sin^2x = 1
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Your 2's are disappearing?
 10 months ago

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

baseballguy1322 Group TitleBest ResponseYou've already chosen the best response.0
How would you convert that to degrees for the final answer?
 10 months ago

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

baseballguy1322 Group TitleBest ResponseYou've already chosen the best response.0
is it 210 and 330 degrees?
 10 months ago

myininaya Group TitleBest 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
 10 months ago

myininaya Group TitleBest 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.
 10 months ago

baseballguy1322 Group TitleBest ResponseYou've already chosen the best response.0
so the four answers would be 30, 150, 210, and 330 degrees?
 10 months ago

myininaya Group TitleBest 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.
 10 months ago

myininaya Group TitleBest 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.
 10 months ago

baseballguy1322 Group TitleBest ResponseYou've already chosen the best response.0
okay thanks for the help
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Np. You got it from here?
 10 months ago

baseballguy1322 Group TitleBest ResponseYou've already chosen the best response.0
yeah i got it.
 10 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Neatness.
 10 months ago
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