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Different ways of solving for x in trig. equations

  1. Apr 12, 2014 #1
    1. The problem statement, all variables and given/known data
    According to my math book, I solved the following trig equation correctly:
    1)
    cos3x=0,500=
    3x = 60° + n360°
    x=20+n120°

    2)I also solved this problem correctly:
    4sin^2x -3sin^x= 0
    sinx(4sinx-3)=0
    x=n*360°
    or
    4sinx=3
    sinx=3/4
    x= ca. 49°
    x=49° + n360° or 131+ n360°.

    Now I´m wondering why I can´t solve question nr 1) in the following way:
    cosx = 0,500/3
    x=80°
    x=80° + n360°

    i.e. why can´t I solve question nr 1 the way I did question nr 2?
    I was also wondering if sin2x is the same as 2sinx? does it make a difference where I place the 2?




    2. Relevant equations

    NA

    3. The attempt at a solution

    see above
     
  2. jcsd
  3. Apr 12, 2014 #2

    Curious3141

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    Homework Helper

    Because (in general) ##\cos nx \neq n\cos x##. In fact the expressions for different values of ##n## higher than 1 (like ##n=2## and ##n=3##) are important trigonometric identities.

    In no. 2, you're just factoring out the ##\sin x##. That's completely valid. ##\sin^2 x## is the conventional shorthand for ##(\sin x)^2##. This is the square of the sine of angle ##x##. This is completely different from ##\sin 2x##, which is the sine of the angle ##2x##.

    Huge difference, just like for the cosine.
     
  4. Apr 12, 2014 #3
    Perfect. Now I get it! thanks a lot!
     
  5. Apr 12, 2014 #4

    Fredrik

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    Staff Emeritus
    Science Advisor
    Gold Member

    Check out the graphs:

    cd98f00b204e9800998ecf8427efi199hvhk6&f=HBQTQYZYGY4TSM3EMI3WENBTHAYDCNBVGU3DEMTEGA4GEMZXGEZAaaaa.gif

    To put a 2 in front of sin x is to double the amplitude. To put a 2 in front of the x in sin x is to double the frequency.

    Wolfram Alpha is great for stuff like this.
     
  6. Apr 12, 2014 #5
    Ok, thanks for explaining!
     
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