Question

Find the equation for the graph shown.

Please no direct answers, I'd really like to learn this :)

Answer 1

it looks like the tangent function...

Answer 2

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

Answer 3

okay

Answer 4

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

Answer 5

for the normal tan(a) = y/x

x can not be zero, that occurs at angles, 90 and 270,

Answer 6

okay

Answer 7

or pi and 3pi/2 rad

Answer 8

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

Answer 9

a more general form for the tangent function is

y = A*tan(Bx + C) + D

seen that before?

Answer 10

Yes!

Answer 11

I love those formulas! :D

Answer 12

Wait, don't tell meh

Answer 13

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

Answer 14

No..pi/b is period I thought?

Answer 15

and -c/b is phase shift?

Answer 16

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

Answer 17

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

Answer 18

you will start to see how each changes the thing

Answer 19

I love desmos!

Answer 20

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

Answer 21

okay

Answer 22

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

Answer 23

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

Answer 24

what is the period of the graph

Answer 25

2pi right?

Answer 26

remember, the tangent has a period of pi

Answer 27

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

Answer 28

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

Answer 29

I'm so confused...

Answer 30

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

Answer 31

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

Answer 32

yeah...

Answer 33

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

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

http://prntscr.com/99yqd9

Answer 38

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

Answer 39

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

Answer 40

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

Answer 41

oh...

Answer 42

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

Answer 43

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

Answer 44

Tanks mate

Answer 45

thanks***

Answer 46

welcome, here is a summary shet if you want

Answer 47

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

Answer 48

Thanks...

Answer 49

Trig isn't my friend lol

Answer 50

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

Answer 51

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