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Calculus/Trigonometric equation

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Expert: Alon Mandes - 8/19/2010


Question
Can u show me how to solve these equations. 1.)tan3x=1
2.) cosx+sinxtanx=2 and 3.)cos2x+sinx=0. If you could help me with even one of them i would really appreciate it. thank you.

Answer
1) tan(3x)=1 --> 3x=π/4 --> x=π/12 .
2) cos(x)+sin(x)tan(x)=2 --> cos(x)+sin(x)[sin(x)/cos(x)]=2 -->
  [cos²(x)+sin²(x)]/cos(x)=2 --> 1/cos(x)=2 --> cos(x)=½ -->
   x=π/3 .
3) cos(2x)+sin(x)=0 . We use the trigonometric identity:
  cos(2α)=cos²(α)-sin²(α) , thus : cos²(x)-sin²(x)+sin(x)=0 -->
  We use the tregonometrical identity : cos²(x)=1-sin²(x) , thus :
  1-sin²(x)+sin(x)=0 . Let's set t=sin(x), we get : 1-t²+t=0 .
  The solutions for this equation is : t1=1 AND t2=-½ . Hence,
  # t=1  --> sin(x)=1   --> x=π/2   ("1st solution")
  # t=-½ --> sin(x)=-½  --> x=-π/6  ("2nd solution")

Alon.  

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

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Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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