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anonymous
 one year ago
Find all solutions in the interval [0, 2π).
7 tan3x  21 tan x = 0
anonymous
 one year ago
Find all solutions in the interval [0, 2π). 7 tan3x  21 tan x = 0

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zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Is that \(\large\rm \tan(3x)\) or \(\large\rm \tan^3x\) ? :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm 7\tan^3x21\tan x=0\]Let's factor some stuff first. Looks like they both have..... a tangent... and a 7, ya?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Ok good! Now we apply our `ZeroFactor Property`, setting each individual factor equal to zero, and then solving from there. So our first factor equal to zero is: \(\large\rm 7\tan x=0\)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1You can divide by 7 to simplify things down a bit: \(\large\rm \tan x=0\) Understand how to solve for x in this case? :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would you plug it into a calculator using tan^1?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1I guess you `could` do that :p it's better just remember some of your special angles. tangent is 0 when the angle x is 0.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Oh but I guess umm... they want all of the solutions from 0 to 2pi, so that produces another angle as well.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh yeahhhh, so then pi and 0? or would it be 1/pi and 3/pi?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1sorry got distracted :) um um... yaaaaa, 0 and pi sound good for our first two solutions.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Applying the zerofactor property again:\[\large\rm \tan^2x3=0\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1So ummm... how bout.. add 3. then square root or something, ya?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \tan^2=3\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \tan x=\pm\sqrt{3}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1The positive root 3 will give you 2 angles again. while the negative root 3 will give you 2 more angles! So this solution set is actually giving us 4 angles! kinda crazy.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0uhhhhh... how do you get your solutions from \[\pm \sqrt{3}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Hmm you gotta get better with your unit circle missy! :O http://4.bp.blogspot.com/FMVojhlkcSQ/UInlIKO88oI/AAAAAAAAAC4/fzMOz6di2Y/s1600/image010.jpg So umm.. i couldn't find a really good picture, but here is one.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1The coordinate pair lists first the sine value of that angle, and then the cosine. And then outside of the brackets, on the right, is the tangent value of that angle. So if we look in the first quadrant, it looks like the angle pi/3 gives us sqrt(3), ya?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohhhhh! I see now! :P Thank you so much!
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