Solve this equation on the interval 0$$\le$$ θ

Question

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)

amistre64 · Answer

there is no equation here...

anonymous · Answer

haha really? why is that?

amistre64 · Answer

Its alot of instructions on what to do; but there is no equation to work it on lol

anonymous · Answer

lol!! sorry!!

anonymous · Answer

i got it here

anonymous · Answer

sintheta + sqrt3costheta = 1

amistre64 · Answer

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

anonymous · Answer

yes

amistre64 · Answer

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 · Answer

hahaha thats the way!

anonymous · Answer

damn it im not gettin it!

amistre64 · Answer

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 · Answer

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

amistre64 · Answer

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

anonymous · Answer

ohkay...lol

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

i think ur getin somewhere haha

amistre64 · Answer

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

anonymous · Answer

lol no it isnt haha

amistre64 · Answer

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

anonymous · Answer

would that be the lower value or upper value?

amistre64 · Answer

thats the lower value

anonymous · Answer

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

amistre64 · Answer

its close to 2pi according to the graph

amistre64 · Answer

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 · Answer

11pi/6 right?

amistre64 · Answer

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

anonymous · Answer

howd u get tht?

anonymous · Answer

11pi/6 from -p1/6 ?

amistre64 · Answer

all angles have many names to them because when you walk around a circle you can go along way and still get nowhere

amistre64 · Answer

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 · Answer

lol. so u added two pi?

amistre64 · Answer

I did ;)

anonymous · Answer

haha. it works doesnt it?

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

i do..

anonymous · Answer

yay ur a genius!!! it works haha

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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 · Answer

good ole wolfram lol

anonymous · Answer

so are you a teacher?

amistre64 · Answer

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

anonymous · Answer

good effort. you'll get there mate haha