Mathematics
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OpenStudy (anonymous):
sin2x - 14 sin x + 2 = -5
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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'
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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?
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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):
\[\large \ 7\sin^2 (x) -14 \sin x +2 =-5\]
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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. \[\large x= \frac{-(-2) \pm \sqrt{(-2)^2 -4(1)(1)}}{2}\]\[\large x= \frac{2}{2} = 1\]
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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.
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OpenStudy (anonymous):
we already know
|dw:1371530910398:dw|
where X=sinx