haleyelizabeth2017
  • haleyelizabeth2017
Find the equation for the graph shown. Please no direct answers, I'd really like to learn this :)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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haleyelizabeth2017
  • haleyelizabeth2017
1 Attachment
DanJS
  • DanJS
it looks like the tangent function...
DanJS
  • DanJS
recall, the tangent is the opposite over adjacemt, or tan(a) = y/x on the unit circle

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haleyelizabeth2017
  • haleyelizabeth2017
okay
DanJS
  • DanJS
the vertical lines are where the tangent is undefined, when x=0, you can't have 0 in the denominator
DanJS
  • DanJS
for the normal tan(a) = y/x x can not be zero, that occurs at angles, 90 and 270,
haleyelizabeth2017
  • haleyelizabeth2017
okay
DanJS
  • DanJS
or pi and 3pi/2 rad
haleyelizabeth2017
  • haleyelizabeth2017
We can already tell that there will be no vertical shift...
DanJS
  • DanJS
a more general form for the tangent function is y = A*tan(Bx + C) + D seen that before?
haleyelizabeth2017
  • haleyelizabeth2017
Yes!
haleyelizabeth2017
  • haleyelizabeth2017
I love those formulas! :D
haleyelizabeth2017
  • haleyelizabeth2017
Wait, don't tell meh
DanJS
  • DanJS
A is amplitude B is period C is phase shift D is vertical shift
haleyelizabeth2017
  • haleyelizabeth2017
No..pi/b is period I thought?
haleyelizabeth2017
  • haleyelizabeth2017
and -c/b is phase shift?
haleyelizabeth2017
  • haleyelizabeth2017
I'm so confused...period is the only thing different between tan and cos/sin functions..
DanJS
  • DanJS
graph y=a*(b*x + c) + d here and hit create for all 4 a,b,c,d then slide around the values https://www.desmos.com/calculator
DanJS
  • DanJS
you will start to see how each changes the thing
haleyelizabeth2017
  • haleyelizabeth2017
I love desmos!
DanJS
  • DanJS
y=tan(x) is just when a,b, = 1 and c.d = 0
haleyelizabeth2017
  • haleyelizabeth2017
okay
haleyelizabeth2017
  • haleyelizabeth2017
Would it be like y=tan(1/2x + something) ?
haleyelizabeth2017
  • haleyelizabeth2017
Wait...y=tan(1/2x+1pi/2) correct?
DanJS
  • DanJS
what is the period of the graph
haleyelizabeth2017
  • haleyelizabeth2017
2pi right?
DanJS
  • DanJS
remember, the tangent has a period of pi
haleyelizabeth2017
  • haleyelizabeth2017
yeah, but the graph has a period of 2pi it looks like...
DanJS
  • DanJS
it repeats every pi rad for tan(x), and so does that graph, the period is not changed
haleyelizabeth2017
  • haleyelizabeth2017
I'm so confused...
haleyelizabeth2017
  • haleyelizabeth2017
If it was every pi, it would be at 0 and 2pi as well
DanJS
  • DanJS
unlike sin and cos whose period is a full circle 2pi, the tangent has a period of pi.
haleyelizabeth2017
  • haleyelizabeth2017
yeah...
DanJS
  • DanJS
the graph also has a period of pi, notice each time it crosses the x-axis it is pi further
DanJS
  • DanJS
the period is unchanged B=1, it is not shifted up/down D=0
haleyelizabeth2017
  • haleyelizabeth2017
I know it doesn't have a vertical shift...
DanJS
  • DanJS
tan(x) crosses the x axis when y=tan(x) = 0 , or when sin(x)=0
haleyelizabeth2017
  • haleyelizabeth2017
http://prntscr.com/99yqd9
DanJS
  • DanJS
the graph of the normal tan(x) function has vertical asmytopes at pi/2 +n*pi/2 points it crosses the x-axis at 0, pi , 2pi ...n*pi
DanJS
  • DanJS
this graph is not shifted up/down, or left, right
DanJS
  • DanJS
it is just the graph of y = tan(x)
haleyelizabeth2017
  • haleyelizabeth2017
oh...
DanJS
  • DanJS
yeah, the amplitude is also 1, recall the tangent(pi/4) = 1, here it is for every pi/4 past the intercepts
DanJS
  • DanJS
maybe go through these short vids to understand a bit better.. https://www.khanacademy.org/math/trigonometry/trig-function-graphs
haleyelizabeth2017
  • haleyelizabeth2017
Tanks mate
haleyelizabeth2017
  • haleyelizabeth2017
thanks***
DanJS
  • DanJS
welcome, here is a summary shet if you want
DanJS
  • DanJS
once you learn the unit circle and what it is, that is pretty much trig , everything is kinda from that
haleyelizabeth2017
  • haleyelizabeth2017
Thanks...
haleyelizabeth2017
  • haleyelizabeth2017
Trig isn't my friend lol
DanJS
  • DanJS
it will click one day, probably after the class is over and you doing other maths.. lol that how it works
haleyelizabeth2017
  • haleyelizabeth2017
LOL yep! It sucks...the time you need it to make sense it doesn't x'D...I was like this last year with Algebra 2 haha

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