A community for students.
Here's the question you clicked on:
 0 viewing
baseballguy1322
 2 years ago
Please help! solve: 4sin³x+2sin²x2sinx1=0 for 0° ≤ x ≤ 360°
baseballguy1322
 2 years ago
Please help! solve: 4sin³x+2sin²x2sinx1=0 for 0° ≤ x ≤ 360°

This Question is Closed

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

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

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

baseballguy1322
 2 years 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
 2 years 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
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.2or you could factor by grouping :) much simpler

baseballguy1322
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.2\[(4\sin^3(x)+2\sin^2(x))+(2\sin(x)1)=0\]

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

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

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

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

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

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

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

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

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

myininaya
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0How would you convert that to degrees for the final answer?

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

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

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

myininaya
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0okay thanks for the help

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.2Np. You got it from here?
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.