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

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

Hi All,

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.pdf

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

Originally Posted by dannybongo
Hi All,

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.pdf
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

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

Hi,

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 haven’t tackled many equations with trig involved

The expression is 2*pi*2*t

Thanks

4. ## 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

$\displaystyle t = 0.2468$

5. ## 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!

6. ## 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.)