Find the equation for the graph shown.
Please no direct answers, I'd really like to learn this :)

- haleyelizabeth2017

Find the equation for the graph shown.
Please no direct answers, I'd really like to learn this :)

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- schrodinger

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- haleyelizabeth2017

##### 1 Attachment

- DanJS

it looks like the tangent function...

- DanJS

recall, the tangent is the opposite over adjacemt, or tan(a) = y/x on the unit circle

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## More answers

- haleyelizabeth2017

okay

- DanJS

the vertical lines are where the tangent is undefined, when x=0, you can't have 0 in the denominator

- DanJS

for the normal tan(a) = y/x
x can not be zero, that occurs at angles, 90 and 270,

- haleyelizabeth2017

okay

- DanJS

or pi and 3pi/2 rad

- haleyelizabeth2017

We can already tell that there will be no vertical shift...

- DanJS

a more general form for the tangent function is
y = A*tan(Bx + C) + D
seen that before?

- haleyelizabeth2017

Yes!

- haleyelizabeth2017

I love those formulas! :D

- haleyelizabeth2017

Wait, don't tell meh

- DanJS

A is amplitude
B is period
C is phase shift
D is vertical shift

- haleyelizabeth2017

No..pi/b is period I thought?

- haleyelizabeth2017

and -c/b is phase shift?

- haleyelizabeth2017

I'm so confused...period is the only thing different between tan and cos/sin functions..

- 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

you will start to see how each changes the thing

- haleyelizabeth2017

I love desmos!

- DanJS

y=tan(x) is just when a,b, = 1 and c.d = 0

- haleyelizabeth2017

okay

- haleyelizabeth2017

Would it be like y=tan(1/2x + something) ?

- haleyelizabeth2017

Wait...y=tan(1/2x+1pi/2) correct?

- DanJS

what is the period of the graph

- haleyelizabeth2017

2pi right?

- DanJS

remember, the tangent has a period of pi

- haleyelizabeth2017

yeah, but the graph has a period of 2pi it looks like...

- DanJS

it repeats every pi rad for tan(x), and so does that graph, the period is not changed

- haleyelizabeth2017

I'm so confused...

- haleyelizabeth2017

If it was every pi, it would be at 0 and 2pi as well

- DanJS

unlike sin and cos whose period is a full circle 2pi, the tangent has a period of pi.

- haleyelizabeth2017

yeah...

- DanJS

the graph also has a period of pi, notice each time it crosses the x-axis it is pi further

- DanJS

the period is unchanged B=1, it is not shifted up/down D=0

- haleyelizabeth2017

I know it doesn't have a vertical shift...

- DanJS

tan(x) crosses the x axis when y=tan(x) = 0 , or when sin(x)=0

- haleyelizabeth2017

http://prntscr.com/99yqd9

- 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

this graph is not shifted up/down, or left, right

- DanJS

it is just the graph of y = tan(x)

- haleyelizabeth2017

oh...

- DanJS

yeah, the amplitude is also 1, recall the tangent(pi/4) = 1, here it is for every pi/4 past the intercepts

- DanJS

maybe go through these short vids to understand a bit better..
https://www.khanacademy.org/math/trigonometry/trig-function-graphs

- haleyelizabeth2017

Tanks mate

- haleyelizabeth2017

thanks***

- DanJS

welcome, here is a summary shet if you want

##### 1 Attachment

- DanJS

once you learn the unit circle and what it is, that is pretty much trig , everything is kinda from that

- haleyelizabeth2017

Thanks...

- haleyelizabeth2017

Trig isn't my friend lol

- DanJS

it will click one day, probably after the class is over and you doing other maths.. lol that how it works

- 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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