anonymous one year ago Find all solutions in the interval [0, 2π). sin2 x + sin x = 0

1. anonymous

2. 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

3. anonymous

I am very confused

4. anonymous

5. 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

6. 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.

7. 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

8. Australopithecus

Remember that you are only looking for solutions for the interval [0,2pi)

9. anonymous

10. 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?

11. anonymous

x=o,pi,pi/3,2pi/3?

12. 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

13. Australopithecus

Look at the interval 0 to 2pi It is just the top section of the unit circle

14. anonymous

0, pi, 3pi/2

15. Australopithecus

yup

16. anonymous

Thanks!

17. Australopithecus

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18. Australopithecus

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19. anonymous

I will!

20. Australopithecus

21. anonymous

How do you do that?

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23. Australopithecus

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24. Australopithecus

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