Question

Really annoying trigonometric graphing, help!

Answer 1

I need 1,2,5, and 10-24

Answer 2

I'm just not grasping the concept.

Answer 3

f(x) = tan πx/4
g(x) =1/2 sec πx/4

Approximate the interval where f < g.

lets set this up then, we know f and g

tan (πx/4) < 1/2 sec(πx/4)

Answer 4

one thing that might help is to rewrite sec, or maybe even tan. into equivalent terms

Answer 5

how so?

Answer 6

well, tan = sin/cos, right?

and sec = 1/cos .... that might help us see the resemblence

Answer 7

\[\frac{sin (πx/4)}{cos (πx/4)} < \frac{1}{2}\frac{1}{cos(πx/4)}\]

we can get rid of that 1/2 by multiplying by 2

\[\frac{(2)sin (πx/4)}{cos (πx/4)} < \frac{1(2)}{2}\frac{1}{cos(πx/4)}\]

\[\frac{2sin (πx/4)}{cos (πx/4)} < \frac{1}{cos(πx/4)}\]

now it looks better

Answer 8

since the denominators are the same, lets equate numberators

Answer 9

2sin(pi x/4) < 1

Answer 10

so now we graph the equation to find the point?

Answer 11

id stick to the analysis rather than a graph; the graph can be used to dbl chk the results; but i doubt it will give a definitive result

Answer 12

sin (t) < 1/2; well, when does sin(t) = 1/2?

Answer 13

how would we go about the analysis?

Answer 14

divide each side by 2 to get: sin(t) < 1/2

im using "y" to help clean up the argument

Answer 15

"t" that is ... cant type ;)

Answer 16

that's not one of the choices though :/ ,

Answer 17

why would it be? we are only in the middle of it

Answer 18

Hang in there and understand the steps.

Answer 19

OH! Gotcha. I just have a terrible teacher who goes about everything explaining really fast, and then expecting us to know all this. I'm sorry.

Answer 20

it would be good to remember the basic angles of trig; i believe this is one of them

Answer 21

sin(t) = 1/2, when t = 30 degrees, or pi/6

Answer 22

is that the special right triangle?

Answer 23

it is

Answer 24

i have to remember the interval:

-pi/4 to pi/4, that is between 45 and -45 degrees if i recall it correctly

Answer 25

now i would see about equating pi x/4 and t

pi x/4 = pi/6

divide off the pis

x/4 = 1/6

and multiply off the 1/4

x = 4/6 , and simplify

x = 2/3

so, if i did it right, it should be (-1, 2/3)

but if you have questions as to why, it would be good to ask. The numbers tend to be unimportant and it is the process that matters.

Answer 26

why the -1?

Answer 27

its part of our initial interval; and sin(pi *-1/4) is less than 1/2

Answer 28

i see. so for number 2 i would just multiply our original interval?

Answer 29

it would be nice if we could, but no.

trig functions are periodic, they do not act like linear functions. so its best to retrace the steps to make sure

Answer 30

or would it not change?

Answer 31

2f just changes how high or low the graph would go; so id guess that its the same intervals. But i would still have to dbl chk the results

Answer 32

its not it.

Answer 33

like, number 1 was right, but 2f changed it in some way, because now it's not the same

Answer 34

\[2*\frac{sin (πx/4)}{cos (πx/4)} < 2*\frac{1}{2}\frac{1}{cos(πx/4)}\]

\[\frac{2sin (πx/4)}{cos (πx/4)} < \frac{1}{cos(πx/4)}\]

\[2sin (πx/4) < 1\]

\[sin (πx/4) < 1/2\]

it looks to be the same

Answer 35

must be a problem with the software. now for number 5,i cant tell the graphs apart

Answer 36

which one is number 5? this thing is hard to follow

Answer 37

graph for y=csc (x)

Answer 38

well, I know csc is the humpbacks of sine