
Complex Analysis Complex Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 11th, 2017, 12:46 PM  #1 
Newbie Joined: Jan 2017 From: Canada Posts: 20 Thanks: 0  Prove that sin(z) <= 3 and z<=1
How do I solve this please?

February 11th, 2017, 12:55 PM  #2 
Senior Member Joined: Sep 2015 From: CA Posts: 1,207 Thanks: 614 
there has to be more to this problem than what you've written do you mean show that $z\leq 1 \Rightarrow \sin(z) \leq 3 ,~\forall z \in \mathbb{C}~?$ 
February 11th, 2017, 01:05 PM  #3 
Senior Member Joined: Sep 2016 From: USA Posts: 114 Thanks: 44 Math Focus: Dynamical systems, analytic function theory, numerics 
I'll assume you mean what Romsek said which is the only reasonable thing I can think you might. You can show this by noticing that $e^z = e^{\Re(z)}$ and using the expression $$ \sin(z) = \frac{e^{iz}  e^{iz}}{2i}.$$ I'll leave you to the details as they are straightforward. 
February 13th, 2017, 01:18 PM  #4 
Newbie Joined: Jan 2017 From: Canada Posts: 20 Thanks: 0  

Tags 
<, <, prove, sinz, z<1, z<1 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Prove this PLEASE HELP  Deiota  Real Analysis  4  March 25th, 2013 09:13 AM 
Prove  Rekooo  Algebra  1  December 28th, 2010 03:38 PM 
Goldbach's conjecture (to prove or not to prove)  octaveous  Number Theory  13  September 23rd, 2010 04:36 AM 
prove prove prove. currently dont know where to post  qweiop90  Algebra  1  July 31st, 2008 06:27 AM 
prove prove prove. currently dont know where to post  qweiop90  New Users  1  January 1st, 1970 12:00 AM 