Split (1)

train · 116k rows

role stringclasses 2 values	content stringlengths 0 2.1k	session_id int64 10 21.7k	sequence_id int64 0 2.38k	annotations listlengths 0 8
volunteer	this is based on a normalized A=1	21,572	60	[]
volunteer	so A>1 stretch 0<A<1 shrink	21,572	61	[]
student	got it	21,572	62	[]
volunteer	sorry	21,572	63	[]
volunteer	\|A\|	21,572	64	[]
volunteer	so \|A\|>1 stretch 0<\|A\|<1 shrink	21,572	65	[]
volunteer	A can be negative as well	21,572	66	[]
volunteer	can you see the graphs im sharing?	21,572	67	[]
student	yes	21,572	68	[]
volunteer	If you can see the blue graph	21,572	69	[]
volunteer	A>1	21,572	70	[]
volunteer	So it gets stretched	21,572	71	[]
volunteer	I switched to A=10 to make it more obvious	21,572	72	[]
volunteer	yellow is the standard tanx graph	21,572	73	[]
volunteer	green is when 0<A<1	21,572	74	[]
volunteer	see how it is squeezed vertically	21,572	75	[]
volunteer	A<0 flips tan around y-axis	21,572	76	[]
student	yes its like hugging the x axis more	21,572	77	[]
volunteer	'hug' was the exact word I was thinking but didn't want to confuse	21,572	78	[]
volunteer	you	21,572	79	[]
volunteer	purple is a negative amplitude	21,572	80	[]
volunteer	all that to say that amplitude is A	21,572	81	[]
volunteer	now back to our question	21,572	82	[]
volunteer	how to find A	21,572	83	[]
volunteer	easiest way is to find where pi/4 is	21,572	84	[]
volunteer	on x-axis	21,572	85	[]
volunteer	as tanpi/4 = 1	21,572	86	[]
student	pi/4?	21,572	87	[]
student	oh	21,572	88	[]
volunteer	now, what 'pi/4' is depends on the phase shift and what B is	21,572	89	[]
volunteer	'pi/4' is dependent on the period	21,572	90	[]
volunteer	you can think of it as period over 4	21,572	91	[]
student	okay	21,572	92	[]
student	we git that the period was pi/6 rigjt	21,572	93	[]
volunteer	right	21,572	94	[]
volunteer	so it would be what for this problem	21,572	95	[]
volunteer	?	21,572	96	[]
volunteer	the important x-value	21,572	97	[]
volunteer	hello?	21,572	98	[]
student	i dont understand	21,572	99	[]
volunteer	what would (pi/6)/4 be?	21,572	100	[]
student	ohh	21,572	101	[]
student	pi over 24	21,572	102	[]
volunteer	right	21,572	103	[]
volunteer	so what is the y-value for pi/24	21,572	104	[]
student	3?	21,572	105	[]
volunteer	that's what I get	21,572	106	[]
volunteer	Now put it all together into the general form of tanx and what is the function?	21,572	107	[]
student	y = A tan(B(x - C)) + D	21,572	108	[]
volunteer	yes	21,572	109	[]
volunteer	plug in the values	21,572	110	[]
student	is A = 3?	21,572	111	[]
volunteer	for 'ABCD'	21,572	112	[]
volunteer	yes	21,572	113	[]
student	y = 3 tan(6x)	21,572	114	[]
volunteer	Another tip for finding the amplitude	21,572	115	[]
volunteer	You need at least one data point that is not on the x-axis	21,572	116	[]
volunteer	so I recommended using the period/4	21,572	117	[]
volunteer	You may not always need this as they may give you some (x,y)	21,572	118	[]
volunteer	Then once you find the shifts and phase	21,572	119	[]
student	wdym by one data point not on x axis	21,572	120	[]
volunteer	assuming you don't have a vertical shift or 'D=0'	21,572	121	[]
volunteer	using a point of form (0,y)	21,572	122	[]
volunteer	Wont help you find A	21,572	123	[]
volunteer	as y=Atan(0) = 0	21,572	124	[]
student	ohh	21,572	125	[]
volunteer	you want x=/=0	21,572	126	[]
volunteer	so that you can calculate A in form A=y/tan(bx-c)	21,572	127	[]
volunteer	now if you do have a vertical shift	21,572	128	[]
volunteer	A = (y-D)/tan(bx-c)	21,572	129	[]
volunteer	I can show you this on the boad	21,572	130	[]
volunteer	board*	21,572	131	[]
student	yes please	21,572	132	[]
volunteer	does that makes sense?	21,572	133	[]
volunteer	we used the point (pi/24 , 3) for this problem	21,572	134	[]
student	yeah	21,572	135	[]
volunteer	does that math make sense?	21,572	136	[]
student	yeah it does	21,572	137	[]
volunteer	Now, this is what my first instinct is to try to get pi/4 inside tan	21,572	138	[]
volunteer	because I know tan(pi/4)=1	21,572	139	[]
volunteer	imagine using the point (pi/10,y)	21,572	140	[]
volunteer	you will need a calculator and then have to use an estimate as the decimal number will be long	21,572	141	[]
student	okay	21,572	142	[]
volunteer	using x=period/4 gives me a cleaner solution	21,572	143	[]
volunteer	another way of thinking it is just to take the distance between the vertical asymptotes and divide by 4	21,572	144	[]
student	will that always work?	21,572	145	[]
volunteer	the distance between vertical asymptotes? yes	21,572	146	[]
volunteer	as that is the period	21,572	147	[]
volunteer	the period/4 will work as well	21,572	148	[]
volunteer	this is a methodology that you will only get from doing it	21,572	149	[]
student	oh right	21,572	150	[]
volunteer	I had to learn it intuitively	21,572	151	[]
student	okay well i have to go now	21,572	152	[]
student	but thank u so much for being patient and helping me with this problem!	21,572	153	[]
volunteer	No problem glad to help	21,572	154	[]
volunteer	was that all the help you needed?	21,572	155	[]
student	for now, yes!	21,572	156	[]
volunteer	great!	21,572	157	[]
student	Hello! How are you? I need help completing a homework assignment that's due soon!	4,385	0	[]
volunteer	Hi	4,385	1	[]

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