A community for students.
Here's the question you clicked on:
 0 viewing
thrustfault
 2 years ago
Let f(x) = sin(x) + icos(x). Show that f(x) = 1.
I'm not even sure where to start here...
thrustfault
 2 years ago
Let f(x) = sin(x) + icos(x). Show that f(x) = 1. I'm not even sure where to start here...

This Question is Closed

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0hey its too much easy... f(x)=sqrt((1)^2+(1)^2)=sqrt(2)

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0here we will take its real part 1 will cos(x) and also 1 from imagnary part i(sinx) hey u have written wrong equation.. its cos(x)isin(x)

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0The question is right. I know DeMoivres, but in this case it's sin(x) + icos(x).

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0ah oookkk ya its absolute value

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0So far I have LHS = \[\frac{ e ^{ix}e^{ix} }{ 2 } + \frac{ e ^{ix}+e^{ix} }{ 2 }i\] Have I completely overthought the problem ? :)

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0no i is denominator from demorvie`s, but in this case I did`nt get u how u got this result

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0ok am gonna solve its prove and implement according to this condition the `ll msg u here ok

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks :) I'm so confused...

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0hahahhah i just wanna say write i in denominator ok i mean (eix−e−ix)2+(eix+e−ix)2i

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0Hmm... I don't get it. How does that show that sin(x) + icos(x) = 1?

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0oh i see wait i solve it and post the diagrame okk buddy

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0daer i can`t .. i have seen the same result for it sqareroot 2 iz answer for both condition.. cos when we see cosx+isinx,, or sinx+icosx... taking coifficients we get the same result..

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0i thinks its wrong question or some thing missing ... can u give the link where did u got it from ???

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0Yep, it's question 1 iv) from this paper: http://www.scribd.com/doc/112148611/MATH1131Mathematics1A1 Thanks :)

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0http://www.mathwarehouse.com/ellipse/equationofellipse.php http://www.algebra.com/algebra/homework/equations/THEO20100329.lesson

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0u got ur answer or not /??

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0Nope, heh. Not yet :(

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0ok if its difficault then msg me ur question i will solve it my self and will post the pic here ok

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah I don't know how to get the function to = 1...

AccessDenied
 2 years ago
Best ResponseYou've already chosen the best response.1I am thinking that you are using the fact that f(x) represents the exact distance between it and 0 on the complex plane... Notice that you can create a right triangle with the real part of f(x) and the imaginary part of x on a complex plane: dw:1352104120632:dw So, here, Re(f) = sin(x) and Im(f) = cos(x). We drop off the i since we're dealing with distances only for the imaginary part. Using Pythagorean theorem, f(x)^2 = (Re(f))^2 + (Im(f))^2 = sin^2 x + cos^2 x. Since we have a neat trigonometric identity here, we can use it to reduce sin^2 x + cos^2 x as 1. Take the square root of both sides and we're done. :)

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks so much for your clear and concise answer!! I've been stuck on this question for a long time :)

AccessDenied
 2 years ago
Best ResponseYou've already chosen the best response.1You're welcome! :)

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.1perhaps this definition can refresh you \[\huge \left a + bi \right=a^2+b^2 \]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.