Mathematics
6 Online
OpenStudy (anonymous):
3tanx3-10tanx=0 , in the domain 180
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OpenStudy (anonymous):
excuse me is it tan3x or tanx3
OpenStudy (anonymous):
tanx^3
OpenStudy (anonymous):
sorry i mean tanx^2
OpenStudy (anonymous):
so 2tanx^2 -10tanx
OpenStudy (anonymous):
omggg 3tanx^2 -10tanx
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OpenStudy (anonymous):
@nincompoop
OpenStudy (anonymous):
@abb0t
jimthompson5910 (jim_thompson5910):
Is it \[\Large 3\tan(x^2) - 10\tan(x)=0\]
or
Is it \[\Large 3\left(\tan(x)\right)^2 - 10\tan(x)=0\]
??
OpenStudy (anonymous):
the second one
jimthompson5910 (jim_thompson5910):
you can let z = tan(x)
that gives
\[\Large 3z^2 - 10z = 0\]
\[\Large z(3z - 10) = 0\]
agreed?
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OpenStudy (anonymous):
actually the x is the angle sign
OpenStudy (anonymous):
yep i get those steps dk what to di next
jimthompson5910 (jim_thompson5910):
so if z(3z-10) = 0, then either z = 0 or 3z-10 = 0 by the zero product property
jimthompson5910 (jim_thompson5910):
re-substitute in z = tan(x)
z = 0 turns into tan(x) = 0
3z-10 = 0 turns into 3*tan(x) - 10 = 0
OpenStudy (anonymous):
jim we need to consider the xrange of x
i also got here but the range got me confused
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jimthompson5910 (jim_thompson5910):
true, that's a good point
OpenStudy (anonymous):
ok i get this whats next
jimthompson5910 (jim_thompson5910):
solve tan(x) = 0 and 3*tan(x) - 10 = 0
and make sure 180<x<360
jimthompson5910 (jim_thompson5910):
use the arctan function on a calculator to undo the tan function
OpenStudy (anonymous):
or we can put the range
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OpenStudy (anonymous):
tan 0 i get 0 , for other i get 73.300
jimthompson5910 (jim_thompson5910):
is x = 0 in the interval 180<x<360 ?
jimthompson5910 (jim_thompson5910):
is x = 73.3 in the interval 180<x<360 ?
OpenStudy (anonymous):
umm
OpenStudy (anonymous):
yea that the part i am stuck on
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jimthompson5910 (jim_thompson5910):
if it is, then you can keep the solution
if not, then add/subtract 180 until you get in the interval
jimthompson5910 (jim_thompson5910):
being in the interval means that the number is between 180 and 360
OpenStudy (anonymous):
ok 73 is
jimthompson5910 (jim_thompson5910):
nope, 73 is not between 180 and 360
OpenStudy (anonymous):
no i mean when i add 180
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jimthompson5910 (jim_thompson5910):
oh ok
OpenStudy (anonymous):
excuse since its periodic the range can be taken in 0<x<180
or 0<x<2pie
OpenStudy (anonymous):
k got the answer thank you
jimthompson5910 (jim_thompson5910):
no problem
OpenStudy (anonymous):
thanks jim
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OpenStudy (anonymous):
u guy can stick around ? i got more
OpenStudy (anonymous):
oky woul love to in any way