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Mathematics 15 Online
OpenStudy (anonymous):

sin2x - 14 sin x + 2 = -5

OpenStudy (anonymous):

solve for x?

OpenStudy (anonymous):

solve for sin x

OpenStudy (anonymous):

is the first term \[\sin^2x\]

OpenStudy (anonymous):

yes sorry my bad

OpenStudy (anonymous):

i call this a batman quadratic. 'a quadratic in disguise'

OpenStudy (jhannybean):

\[\large \sin^2 (x) -14 \sin x +2 =-5 \] think about \[\large ax^2 +bx+ c= 0\] and solve it like a quadratic.

OpenStudy (anonymous):

Find all solutions to the equation. would it be sin x=1?

OpenStudy (jhannybean):

lol chris.

OpenStudy (anonymous):

thats wat mi teacher used to say

OpenStudy (jhannybean):

Or maaybe you can solve it by completing the square?

OpenStudy (anonymous):

ohhh snhnap i forgot to add the 7

OpenStudy (anonymous):

7 sin^2x - 14 sin x + 2 = -5

OpenStudy (jhannybean):

?...

OpenStudy (anonymous):

sorry -.-

OpenStudy (jhannybean):

\[\large \ 7\sin^2 (x) -14 \sin x +2 =-5\]

OpenStudy (anonymous):

that would make sense. thats easier.

OpenStudy (anonymous):

add 5 to both sides then divide 7 to both sides.

OpenStudy (anonymous):

sin^2(x)-2sinx+1 sinx(sinx-1)?

OpenStudy (anonymous):

i feel like jhannybean is going to solve this nicely.

OpenStudy (jhannybean):

Yeah...we can solve it utilizing the quadratic equation. first,move the -5 to the other side. \[\large \ \frac{7\sin^2 (x)}{7} -\frac{14 \sin( x)}{7} +\frac{7}{7} =0\]\[\large \sin^2(x) -2\sin(x)+1=0\] quadratic formula. \[\large x= \frac{-(-2) \pm \sqrt{(-2)^2 -4(1)(1)}}{2}\]\[\large x= \frac{2}{2} = 1\]

OpenStudy (jhannybean):

Oh did i forget something...

OpenStudy (anonymous):

sinx=1?

OpenStudy (jhannybean):

How would you solve this, chris?

OpenStudy (anonymous):

kk.

OpenStudy (jhannybean):

Yes i believe im solving it the right way, lol.

OpenStudy (anonymous):

we already know |dw:1371530910398:dw| where X=sinx

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