Babybee24
cos^2(x)+cos(x)sin(x)=0 solve for x



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myininaya
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Try factoring

Babybee24
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I factored a cos(x) out but then im stuck

myininaya
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cos(x)( ? + ? ) =0
So what should be in the places of those ?'s once you factor out cos(x)?

Babybee24
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cos(x)(cosx+sinx)

myininaya
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Yes. Set both factors equal to 0.
cos(x)=0 ; cos(x)+sin(x)=0

myininaya
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Solve cos(x)=0 for x
And find the value x so that cos(x) and sin(x) are opposites (i.e cos(x)=sin(x))

Babybee24
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cosx=pie/2 ?

myininaya
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cos(x)=0 for x=pi/2
cos(x) does not equal pi/2
But one value that satisfies cos(x)=0 is x=pi/2
Are there any other values?

Babybee24
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x=3pi/2

myininaya
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Ok and you can also say we have x=pi/2+2npi where n is an integer
or x=3pi/2+2n pi where n is an integer

myininaya
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We also need to find the values of x where cos(x) and sin(x) have opposite values.

myininaya
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dw:1357920385873:dw
As you can see they will be opposite in quadrant 2 and 4.

myininaya
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dw:1357920430907:dw
These points is where cos(x) and sin(x) are opposite. Now what angle are these points at from the initial ray?

Babybee24
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135 and 315?

myininaya
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Correct.

myininaya
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Now should your answer be in radians or degrees?

Babybee24
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um radians?

myininaya
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So 135*pi/180
or
315*pi/180

myininaya
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Don't forget we can go around the circle infinitely many times from those angles.

myininaya
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So 135pi/180+2npi , 315pi/180+2npi

myininaya
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Don't forget the other solutions we wrote above.
Good job. :)

Babybee24
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thanks!