anonymous
  • anonymous
Find all solutions in the interval [0, 2π). sin2 x + sin x = 0
Mathematics
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
i give medals! please help!
anonymous
  • anonymous
you can factor the common term of sin x sin² x + sin x = 0 (sin x)(sin x + 1) = 0 Now set both factors equal to 0 and solve these two equations sin x = 0 sin x + 1 = 0
anonymous
  • anonymous
I am very confused

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
i only have a few more minutes to answer this please help and explain!
Australopithecus
  • Australopithecus
So you have, \[\sin^2(x) + \sin(x) = 0\] By the definition of a exponent \[x^2 = x*x\] etc so, \[\sin^2(x) + \sin(x) = 0\] can be written as: \[\sin(x)\sin(x) + \sin(x) = 0\] Now you can factor out sin(x): \[\sin(x)(\sin(x) + 1) = 0\] Now look at both terms sin(x) and (1 + sin(x)) When one of them equals 0 you have a solution
anonymous
  • anonymous
sin² x and sin x have a common term of sin x so it can be factored out giving the equation as (sin x)(sin x + 1) = 0 If two thing multiply to be 0, one or both of them is 0. so we can write thes the two equations sin x = 0 and sin x + 1 = 0 To solve sin x = 0, look on the unit circle and pick out all the angle where sine is 0. To solve sin x + 1 = 0, subtract the 1 from both sides sin x = -1 now pick out the angles that have a sine of -1.
Australopithecus
  • Australopithecus
so for (1 + sin(x)) = 0 sin(x) must equal - 1 what value of x makes sin(x) = -1? For the second term sin(x) = 0 what value of x makes sin(x) equal 0 Look at the graph of sin(x) http://www.wolframalpha.com/input/?i=graph+of+sin%28x%29+between+0+and+2pi
Australopithecus
  • Australopithecus
Remember that you are only looking for solutions for the interval [0,2pi)
anonymous
  • anonymous
is there answer x= 0,pi,4pi/3,5pi/3?
anonymous
  • anonymous
0 and pi are solutions to sin x = 0. the other two aren't solutions to either equation. Where is sine equal to -1 between 0 and 2pi?
anonymous
  • anonymous
x=o,pi,pi/3,2pi/3?
Australopithecus
  • Australopithecus
when x = 0 sin(0) = 0 so x =0 is a solution sin(4pi/3) does not equal 0 or -1 so it is not a solution sin(5pi/3) does not equal 0 or -1 so it is not a solution sin(pi) = 0 so it is a solution
Australopithecus
  • Australopithecus
Look at the interval 0 to 2pi It is just the top section of the unit circle
1 Attachment
anonymous
  • anonymous
0, pi, 3pi/2
Australopithecus
  • Australopithecus
yup
anonymous
  • anonymous
Thanks!
Australopithecus
  • Australopithecus
If you found my help useful please rate me using the qualified help located at the top
Australopithecus
  • Australopithecus
So I can get paid :)
anonymous
  • anonymous
I will!
Australopithecus
  • Australopithecus
Not that I wouldnt have helped you for free :)
anonymous
  • anonymous
How do you do that?
Australopithecus
  • Australopithecus
http://i.imgur.com/7yfPY5A.jpg
Australopithecus
  • Australopithecus
Click this button :)
Australopithecus
  • Australopithecus
Ha brain is in stupid mode right now Click rate qualified helper so the button next to it

Looking for something else?

Not the answer you are looking for? Search for more explanations.