Question

Find all solutions in the interval [0, 2π).

sin2 x + sin x = 0

Answer 1

i give medals! please help!

Answer 2

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

Answer 3

I am very confused

Answer 4

i only have a few more minutes to answer this please help and explain!

Answer 5

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

Answer 6

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.

Answer 7

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

Answer 8

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

Answer 9

is there answer x= 0,pi,4pi/3,5pi/3?

Answer 10

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?

Answer 11

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

Answer 12

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

Answer 13

Look at the interval 0 to 2pi

It is just the top section of the unit circle

Answer 14

0, pi, 3pi/2

Answer 15

yup

Answer 16

Thanks!

Answer 17

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Answer 18

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Answer 19

I will!

Answer 20

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Answer 21

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Answer 22

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Answer 23

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Answer 24

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