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)

- anonymous

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- amistre64

there is no equation here...

- anonymous

haha really? why is that?

- 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

lol!! sorry!!

- anonymous

i got it here

- anonymous

sintheta + sqrt3costheta = 1

- amistre64

sin(t) + sqrt(3)cos(t) = 1 right?

- anonymous

yes

- 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

hahaha thats the way!

- anonymous

damn it im not gettin it!

- 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

http://www.wolframalpha.com/input/?i=Solve%5Bsin%28t%29+%2B+sqrt%283%29cos%28t%29+%3D%3D+1%2Ct%5D

- amistre64

an alternative form is:
\[4\sin[\frac{\pi}{4}-\frac{t}{2}] . \sin[\frac{t}{2}+\frac{\pi}{12}]=0\]

- anonymous

ohkay...lol

- amistre64

since sin = 0 at 0 and pi; we can prolly figure out a few t's from this ?

- amistre64

t/2 = pi/4
t = pi/2sounds reasoneable plug it into the orifinal and test

- anonymous

i think ur getin somewhere haha

- amistre64

the other seems to be -pi/6 but that aint in the inteval is it lol

- anonymous

lol no it isnt haha

- amistre64

sin(pi / 2) + (sqrt(3) * cos(pi / 2)) = 1 is good tho

- anonymous

would that be the lower value or upper value?

- amistre64

thats the lower value

- anonymous

i only get two shots so i probably beta wait till we figur out the upper value lol

- amistre64

its close to 2pi according to the graph

- 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

11pi/6 right?

- amistre64

sin((11 * pi) / 6) + (sqrt(3) * cos((11 * pi) / 6)) = 1: from google

- anonymous

howd u get tht?

- anonymous

11pi/6 from -p1/6 ?

- 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

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

lol. so u added two pi?

- amistre64

I did ;)

- anonymous

haha. it works doesnt it?

- amistre64

it does indeed :) becuase they both have the same values

- anonymous

kay so u reckon i should give pi/2 and 11pi/6 a shot?

- amistre64

i do..

- anonymous

yay ur a genius!!! it works haha

- amistre64

lol .... i had to remember my trigs :)

- anonymous

haha. is there a simpler way of doing this tho?

- 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

good ole wolfram lol

- anonymous

so are you a teacher?

- amistre64

no, just old :) im trying to get my masters degree in math tho so I can teach college math

- anonymous

good effort. you'll get there mate haha

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