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

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jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1can you take common factor on the lefthand side?

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

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

baseballguy1322
 one year ago
Best ResponseYou've already chosen the best response.0You add 1 to the right side but what would the left hand side look like after you simplify the gcf

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

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

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.1yea... I think so @myininaya is correct.. you may have to factor it with the 0 on the righthand side

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

baseballguy1322
 one year ago
Best ResponseYou've already chosen the best response.0Yes I am trying to solve for the possible solutions in degrees. How would you factor by grouping?

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2Look at those first two terms. They have common factor. Look at the last terms. Factor out 1.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2Or you can look at it in terms of u instead of sin at first. Your choice.

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

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

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

baseballguy1322
 one year ago
Best ResponseYou've already chosen the best response.02u^2? or just u^2?

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

baseballguy1322
 one year ago
Best ResponseYou've already chosen the best response.02u^2(2u+1) + ( 2sin) = 0

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

myininaya
 one year ago
Best 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.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2Don'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).

baseballguy1322
 one year ago
Best ResponseYou've already chosen the best response.0Oh yeah that's right, I haven't done factoring in awhile. what would be the next step after this one?

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

baseballguy1322
 one year ago
Best ResponseYou've already chosen the best response.0sin x +1 = 0 sin x = 1 and sin^2x1=0 sin^2x = 1

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

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

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

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

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2You 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

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

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

myininaya
 one year ago
Best 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.

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

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

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

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