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

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

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

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

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

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

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

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

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

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

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

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

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

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

baseballguy1322 Group TitleBest ResponseYou've already chosen the best response.0
2u^21=0
 one year 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).
 one year 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?
 one year ago

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

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

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

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

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

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

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

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

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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Neatness.
 one year ago
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