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--PROBLEM SOLVED--
using the sum and difference identity find the exact value of tan195° and tan345°? For the second one, I know the answer is -2+√3 (its in the book), but i can't derive to it, all i get is a 0 
in case anyone forgot, its this identity:
--the following is for the second problem--
is this the right way to undergo this problem? or do i have to make tan45 into a tan(-45)? Could you show me the steps on how to work out this problem?
edit: made things clearer.
edit2:I thought TL would get it in like 10 min, max. Guess i underestimated the intelligence of TL.
 
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tan195° is tan15° which is tan(45-30)°
tan345° is tan(-15°) which is tan(30-45)°
Use the sum and addition rules to 'expand' the brackets and of course tan45° is 1 and tan30° is root(3)/3
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Draw a trigonometric circle lol.
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tana - tanb
1-tanatanb
is like m1-m2
1-m1m2
same as the area between two lines. o_O
But anyways that should end up to be something like tan(a-b) i.e tan(30-45) = -tan15.
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go back to the basics. proofs
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On May 26 2008 02:52 thoraxe wrote:
edit2:I thought TL would get it in like 10 min, max. Guess i underestimated the intelligence of TL.
Pfft, skyglow did solve it for you in ten mins, only that you didnt understand it.  . But you seem to have problems with using the formula rather than not understanding the problem. So let me clarify a bit...
What skyglow told you that you have to do, and which I htink you have understood, is that you rewrite tan(195) as tan(15) = tan(45-30) and then you use the formula you provided.
Maybe your problem is that you are not clear on what the +- signs means in the formula?
you have tan(a-b). wiht a minus. That means that as the minus is the lower sign in the left hand side of the formula, you have to go on and use the lower sign in the right hand side as well. Doing that, you will get a minus in the nominator of the right hand side, and A PLUS IN THE DENOMINATOR FO THE RIGHT HAND SIDE, not a minus as you have in your op.
Also, to answer your question you asked, you should use tan(45) since the minus is built in the formula in
tan(a-b) --> tan(45 - 30) --> a = +45, b = +30.
+ Show Spoiler [alternate route] +alternatively you could use the forumla with the plus and put the minus in b:
tan(a+b) --> tan(45 + (-30)) --> a=+45, b = -30.
It will give the same result i fyou use the UPPER sign in the formula. You have to use the upper sign as you have a tan(a+b) as oposed to a tan(a-b). Just disregard this spoiler if it confuses you.
So just change the minus to a plus in the denominator of your formula, and you'll be fine. hope that helped, gl.
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problem solved.
since you still don't think the problem is done (i.e. you haven't edited your post saying so), here's the hard part:
your book went through hoops to make it look the way it did.
yw
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On May 26 2008 09:27 wanderer wrote:problem solved. since you still don't think the problem is done (i.e. you haven't edited your post saying so), here's the hard part: your book went through hoops to make it look the way it did. yw
yay, you got it!!!(the first one that actually understood what the problem was asking for, good try everybody though).
Thank you so much, fucking tangent, its the only one that is nerve racking to me. your the best man. btw, I posted my dissapointed in order to spurr up someone's pride in TL's ability to pwn at everything so that someone would've comed to the rescue. i guess my plan did work
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On May 26 2008 08:28 Cascade wrote:Show nested quote +On May 26 2008 02:52 thoraxe wrote:
edit2:I thought TL would get it in like 10 min, max. Guess i underestimated the intelligence of TL. Pfft, skyglow did solve it for you in ten mins, only that you didnt understand it. . But you seem to have problems with using the formula rather than not understanding the problem. So let me clarify a bit... What skyglow told you that you have to do, and which I htink you have understood, is that you rewrite tan(195) as tan(15) = tan(45-30) and then you use the formula you provided. Maybe your problem is that you are not clear on what the +- signs means in the formula? you have tan(a-b). wiht a minus. That means that as the minus is the lower sign in the left hand side of the formula, you have to go on and use the lower sign in the right hand side as well. Doing that, you will get a minus in the nominator of the right hand side, and A PLUS IN THE DENOMINATOR FO THE RIGHT HAND SIDE, not a minus as you have in your op. Also, to answer your question you asked, you should use tan(45) since the minus is built in the formula in tan(a-b) --> tan(45 - 30) --> a = +45, b = +30. + Show Spoiler [alternate route] +alternatively you could use the forumla with the plus and put the minus in b:
tan(a+b) --> tan(45 + (-30)) --> a=+45, b = -30.
It will give the same result i fyou use the UPPER sign in the formula. You have to use the upper sign as you have a tan(a+b) as oposed to a tan(a-b). Just disregard this spoiler if it confuses you. So just change the minus to a plus in the denominator of your formula, and you'll be fine. hope that helped, gl.
OOOOH I SEE NOW, i should've put 1+tan30tan45 on the bottom instead of putting it with a (-) sign. THANK MAN.
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yay, you got it!!!(the first one that actually understood what the problem was asking for, good try everybody though).
Thank you so much, fucking tangent, its the only one that is nerve racking to me. your the best man. btw, I posted my dissapointed in order to spurr up someone's pride in TL's ability to pwn at everything so that someone would've comed to the rescue. i guess my plan did work
lol of course I knew what the problem was asking for, I was just hoping you were capable of doing the problem on your own after realising that 45-30 gives you 15 and 30-45 gives you -15 which was basically everything you needed to do it, but I guess you weren't even capable of that. Expecting the whole thing to be solved for you completely with all the steps is a bit too much.
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On May 26 2008 15:59 skyglow1 wrote:Show nested quote +
yay, you got it!!!(the first one that actually understood what the problem was asking for, good try everybody though).
Thank you so much, fucking tangent, its the only one that is nerve racking to me. your the best man. btw, I posted my dissapointed in order to spurr up someone's pride in TL's ability to pwn at everything so that someone would've comed to the rescue. i guess my plan did work
lol of course I knew what the problem was asking for, I was just hoping you were capable of doing the problem on your own after realising that 45-30 gives you 15 and 30-45 gives you -15 which was basically everything you needed to do it, but I guess you weren't even capable of that. Expecting the whole thing to be solved for you completely with all the steps is a bit too much.
lol stfu i stole your medal fair and square, mister
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The question is trivial if you know the exact form of tan15. We shall do this geometrically.
Construct a triangle of angles, 75,75,30, such that the perpendicular from one of the 75 degree angles is length 1. Keeping in mind the triangle is isosceles, we immediately yield that tan15=2-sqrt3
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On May 30 2008 18:35 wanderer wrote:Show nested quote +On May 26 2008 15:59 skyglow1 wrote:
yay, you got it!!!(the first one that actually understood what the problem was asking for, good try everybody though).
Thank you so much, fucking tangent, its the only one that is nerve racking to me. your the best man. btw, I posted my dissapointed in order to spurr up someone's pride in TL's ability to pwn at everything so that someone would've comed to the rescue. i guess my plan did work
lol of course I knew what the problem was asking for, I was just hoping you were capable of doing the problem on your own after realising that 45-30 gives you 15 and 30-45 gives you -15 which was basically everything you needed to do it, but I guess you weren't even capable of that. Expecting the whole thing to be solved for you completely with all the steps is a bit too much. lol stfu i stole your medal fair and square, mister
yay for you -_-
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