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Trigonometric equation

  • Thread starter GuN
  • Start date
  • #1
GuN
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0

Homework Statement



2 sin(2x) = 2 cos(x)

Homework Equations





The Attempt at a Solution



4sinxcosx-2cosx=0

2(2sinxcosx-cosx)=0

2cosx(sinx-1)=0

2cosx=0 sinx=1


And then I did the math and got pi/2 and 3pi/2 , but that's apparently wrong.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
11,519
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I get cosx * (2*sinx - 1) = 0 for your second to last step. Does that help?
 
  • #3
GuN
9
0
I still get pi/2 and 3 pi/2.

>_<

I'll try consulting my notes on how to properly calculate cosx=0 and sinx=1/2.
 
  • #4
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
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I still get pi/2 and 3 pi/2.
How? You know that ##\sin (\pi/2) = 1## and ##\sin (3\pi/2) = -1##. So obviously neither of those satisfy ##\sin x = 1/2##.
 
  • #5
223
10
arcsin (1/2) = x1
arccos (0) = x2

You have done everything correctly, now you need to figure out what the values for x are. This is not a linear equation, there are 2 series of solutions.

The system I showed you will not be your final answer.
 
  • #6
GuN
9
0
Right, I double checked the notes and found I used the wrong radians.

I redid it and got (for the domain of [0, 2pi] ) pi/6, 5pi/6, pi/2 and 3pi/2.
 

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