anonymous
  • anonymous
Solve this equation on the interval 0\[\le\] θ < 2π. If there is only one solution, write it in the upper box and write NONE in the lower box. If there is no solution, write NONE in both boxes. Round your answer(s) to two decimal places using radians. θ = (smaller value of θ) θ = (larger value of θ)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
there is no equation here...
anonymous
  • anonymous
haha really? why is that?
amistre64
  • amistre64
Its alot of instructions on what to do; but there is no equation to work it on lol

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More answers

anonymous
  • anonymous
lol!! sorry!!
anonymous
  • anonymous
i got it here
anonymous
  • anonymous
sintheta + sqrt3costheta = 1
amistre64
  • amistre64
sin(t) + sqrt(3)cos(t) = 1 right?
anonymous
  • anonymous
yes
amistre64
  • amistre64
then.... sqrt(3)cos(t) = 1 - sin(t) 3cos^2 = 1 +sin^2 -2sin... lets cheat and do this lol http://www.wolframalpha.com/input/?i=sin%28t%29+%2B+sqrt%283%29cos%28t%29+%3D+1
anonymous
  • anonymous
hahaha thats the way!
anonymous
  • anonymous
damn it im not gettin it!
amistre64
  • amistre64
i cant seem to get it out either.... i know theres one answer at least; might have to just make a chart and narrow it in
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=Solve%5Bsin%28t%29+%2B+sqrt%283%29cos%28t%29+%3D%3D+1%2Ct%5D
amistre64
  • amistre64
an alternative form is: \[4\sin[\frac{\pi}{4}-\frac{t}{2}] . \sin[\frac{t}{2}+\frac{\pi}{12}]=0\]
anonymous
  • anonymous
ohkay...lol
amistre64
  • amistre64
since sin = 0 at 0 and pi; we can prolly figure out a few t's from this ?
amistre64
  • amistre64
t/2 = pi/4 t = pi/2sounds reasoneable plug it into the orifinal and test
anonymous
  • anonymous
i think ur getin somewhere haha
amistre64
  • amistre64
the other seems to be -pi/6 but that aint in the inteval is it lol
anonymous
  • anonymous
lol no it isnt haha
amistre64
  • amistre64
sin(pi / 2) + (sqrt(3) * cos(pi / 2)) = 1 is good tho
anonymous
  • anonymous
would that be the lower value or upper value?
amistre64
  • amistre64
thats the lower value
anonymous
  • anonymous
i only get two shots so i probably beta wait till we figur out the upper value lol
amistre64
  • amistre64
its close to 2pi according to the graph
amistre64
  • amistre64
now we know -pi/6 is good; but if we take and try to reach that going from 0 to 2pi what do we get? i wonder
amistre64
  • amistre64
11pi/6 right?
amistre64
  • amistre64
sin((11 * pi) / 6) + (sqrt(3) * cos((11 * pi) / 6)) = 1: from google
anonymous
  • anonymous
howd u get tht?
anonymous
  • anonymous
11pi/6 from -p1/6 ?
amistre64
  • amistre64
all angles have many names to them because when you walk around a circle you can go along way and still get nowhere
amistre64
  • amistre64
we can walk -pi/6 to smell the roses; or we can take the long way around; and walk 11pi/6 to get to the same place to wmell the roses
anonymous
  • anonymous
lol. so u added two pi?
amistre64
  • amistre64
I did ;)
anonymous
  • anonymous
haha. it works doesnt it?
amistre64
  • amistre64
it does indeed :) becuase they both have the same values
anonymous
  • anonymous
kay so u reckon i should give pi/2 and 11pi/6 a shot?
amistre64
  • amistre64
i do..
anonymous
  • anonymous
yay ur a genius!!! it works haha
amistre64
  • amistre64
lol .... i had to remember my trigs :)
anonymous
  • anonymous
haha. is there a simpler way of doing this tho?
amistre64
  • amistre64
i caouldnt find a way to get it into the alternate form; but wolfram did... so i tested that forms results into the original and they worked like a charm
anonymous
  • anonymous
good ole wolfram lol
anonymous
  • anonymous
so are you a teacher?
amistre64
  • amistre64
no, just old :) im trying to get my masters degree in math tho so I can teach college math
anonymous
  • anonymous
good effort. you'll get there mate haha

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