Question

Express this function using defined step-functions please?
\[r=\left\{\begin{array}{lr}
|\sec\theta|
&\mbox{if}&-\frac\pi4<\theta<\frac\pi4
&\mbox{or}&\frac{3\pi}4<\theta<\frac{5\pi}4\\
|\csc\theta|
&\mbox{if}&\frac\pi4<\theta<\frac{3\pi}4
&\mbox{or}&\frac{5\pi}4<\theta<\frac{7\pi}4
\end{array}\right.\]

Answer 1

@primeralph how to disable and enable functions? :O

Answer 2

The piece-wise function\[
f(t) =
\begin{cases}
g(t)& t>a\\
h(t) &t<a
\end{cases}
\]Can be expressed as:\[
f(t) =h(t)+[g(t)-h(t)]H(t-a)
\]
Where \(H(t)\) is the Heaviside function:\[
H(t) =
\begin{cases}
1& t>0\\
0& t<0
\end{cases}
\]

Answer 3

Just keep expanding out using this equation.

Answer 4

Is there no other way than using Heaviside? :/

Answer 5

hey @kc_kennylau!! long time no see it's been about 5 hours!

Answer 6

@DLover243 hi :)

Answer 7

:)

Answer 8

could u help me? :O

Answer 9

sry i don't know math that complecated sry! :(

Answer 10

sec

Answer 11

i'll try

Answer 12

sorry no matchs

Answer 13

lolz

Answer 14

no no matchs i looked it up online

Answer 15

i am trying it. gimme a few sec

Answer 16

this is a creative solution contributed by trollswillrule: \[(1-\lceil \sin4\theta \rceil)(\csc \theta +\sec \theta) \]=f(x)=r

Answer 17

for -45 degrees to 315 degrees

Answer 18

this is to see that 1-the rounded up of sin4theta can become 0 and 1 in each case.

Answer 19

http://www.wolframalpha.com/input/?i=polar+plot+r%3D%281%E2%88%92%E2%8C%88sin4%CE%B8%E2%8C%89%29%28csc%CE%B8%2Bsec%CE%B8%29

Answer 20

just a clarification, if ceiling function of -0.1 is what? is it -1 or 0?

Answer 21

0

Answer 22

Discrete Fourier transform is the best i can think of right now, i dunt think there are easier alternatives anymore...