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Thread: Getting a negative answear for time but cant see where i've gone wrong!

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    Getting a negative answear for time but cant see where i've gone wrong!

    Hi All,

    Please see attached PDF,

    can anyone tell me where I have gone wrong? I'm getting a negative answear for time which cannot be right. When you plot the function, the result I expect to get is 0.2468 (See attached graph). i would much appreciate any help that anyone can provide.

    Thanks
    Query.pdfQuery.pdfGetting a negative answear for time but cant see where i've gone wrong!-graph.png
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    Re: Getting a negative answear for time but cant see where i've gone wrong!

    Quote Originally Posted by dannybongo View Post
    Hi All,

    Please see attached PDF,

    can anyone tell me where I have gone wrong? I'm getting a negative answear for time which cannot be right. When you plot the function, the result I expect to get is 0.2468 (See attached graph). i would much appreciate any help that anyone can provide.

    Thanks
    Query.pdfQuery.pdfClick image for larger version. 

Name:	graph.PNG 
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ID:	39325
    Two things:
    1) Where did the sine term go? It just sort of vanished.

    2) You have the expression $\displaystyle 2 \pi 2 t$. Is that second 2 supposed to be a power or are you just multiplying?

    -Dan
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    Re: Getting a negative answear for time but cant see where i've gone wrong!

    Hi,

    Thanks for your response

    I used the trig rule Tan(x)=Sin(x)/cos(x). When i divided both sides by cos(x) this should change the RHS of the equation from sin(x) into tan(x). I think this is correct, but havenít tackled many equations with trig involved

    The expression is 2*pi*2*t

    Thanks
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    Re: Getting a negative answear for time but cant see where i've gone wrong!

    When you apply arctan you should get
    $\displaystyle 4\pi *t = arctan (\frac{-1}{8\pi})$
    $\displaystyle 4\pi * t= -0.03977 + n\pi$ where n is an integer (remember the periodic nature of trig functions)
    $\displaystyle t = \frac{-0.03977 + n\pi}{4\pi}$

    Taking n=1

    $\displaystyle t = 0.2468$
    Last edited by Debsta; Apr 4th 2019 at 01:50 AM.
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    Re: Getting a negative answear for time but cant see where i've gone wrong!

    Hi debsta,

    Thankyou so much for your help on this. I have to admit I’m not familiar with the n*pi thing. How do you know when do this? I’ve solved equations in the past with arcsin, arctan, etc and not done the pi*n part.

    Thanks again for your help! I plan to go back and brush up on my trig functions and equations with them in

    Cheers!
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    Re: Getting a negative answear for time but cant see where i've gone wrong!

    Consider for example
    tan x = 1

    x=arctan (1)


    Calculator gives $\displaystyle x = \frac{\pi}{4}$

    But because of the cyclic nature of tan, together with the fact that tan x >0 in the first and third quadrants

    $\displaystyle tan(\frac{\pi}{4}) = tan(\frac{\pi}{4} + \pi)= tan(\frac{\pi}{4}+2\pi)= tan(\frac{\pi}{4}+ 3\pi) = ….$

    so

    tan x = 1 has an infinite number of solutions all $\displaystyle \pi$ apart. Same for your equation.

    (Note: a similar concept applies to sin and cos, but it is not as simple as $\displaystyle + n \pi$ because of the quadrants in which those trig functions are pos or neg.)
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