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Babynini
 one year ago
Find all solutions for equation, find solutions in interval [0,2pi)
sq3 tan 3(theta)+1=0
Babynini
 one year ago
Find all solutions for equation, find solutions in interval [0,2pi) sq3 tan 3(theta)+1=0

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Babynini
 one year ago
Best ResponseYou've already chosen the best response.1@peachpi the victory was short lived lol

Babynini
 one year ago
Best ResponseYou've already chosen the best response.13(theta)=arctan(sq3/3) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This is the original? \[\sqrt{3\tan 3\theta+1}=0\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1hm, no. Let me write it out for you :) \[\sqrt{3}\tan3(\theta)+1=0\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1\[\tan3(\theta)=\frac{ \sqrt{3} }{ 3 }\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1So then after quite a bit of simplifying theta = 0.26 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That one's on the unit circle, so they might be looking for an exact answer. π/18, which is about 0.17, so you're right

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1pi/18 is on the unit circle? o.o

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You had 3Θ = arctan (1/√3) 3Θ = π/6 Θ = π/18

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1Why does 3(theta) = pi/6 ?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1sorry, these are probably really elementary questions but I want to make sure and understand.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0because arctan has a domain from pi/2 to pi/2 (because tan positive in the 1st quadrant, negative in the 4th). The angle in that domain with a tan of 1/√3 is π/6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0does that make sense?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1Yeah I just hadn't made the connection so now i've got to think it through a bit :P

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1So now to find it in the right quadrants we add pi?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so this one's a little trickier since the tan is negative. The restriction on the equation is 0 to 2pi, so we actually need to add 2pi to pi/6 to get the 1st solution for 3pi

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We'll have 2 solutions for 3pi between 0 and 2pi: 11π/6 in the 4th quadrant (pi/6 + 2π) 5π/6 in the 2nd quadrant (π/6 + π) dw:1434608981061:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1434609190233:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Dividing each of those by 3 gives Θ = 11π/18 and Θ = 5π/18

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1and those aren't negative.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right. we don't want the negative solutions

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You need to find 3Θ for 0<Θ<6π, so add 2pi to both 5π/6 and 11π/6 twice to get the other 4 solutions for 3Θ

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1so it would be writen as 5pi/18 + 2kpi ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no just 5pi/18. because they gave a specific interval, you don't use 2kpi

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1but we're missing two more quadrants still, right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0there are 4 more solutions. You need to find 3Θ for 0<Θ<6π, so add 2pi to both 5π/6 and 11π/6 twice to get the other 4 solutions for 3Θ

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes. that's a solution dw:1434609720505:dw

Babynini
 one year ago
Best ResponseYou've already chosen the best response.1so our four answers are 5pi/18, 11pi/18. 17pi/18, 23pi/18

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you've got 2 more to go
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