MHB What are the Intercepts of the Sine Wave $y=\sin{2(x-\frac{\pi}{4})}$?

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To find the x-intercepts of the sine wave given by the equation y = sin(2(x - π/4)), set y to 0, leading to the equation 2(x - π/4) = nπ, where n is any integer. This simplifies to x = (nπ/2) + π/4, providing a general solution for the intercepts. The discussion emphasizes that the sine function equals zero at integer multiples of π, thus resulting in infinitely many intercepts. For specific solutions within the range of 0 to 2π, n can take values 0, 1, or 2. The conversation also touches on the correct usage of LaTeX for mathematical expressions.
karush
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$y=\sin{2(x-\frac{\pi}{4})}$

how do you find the x intercepts of this

thot if 0=sin(2x-(pi/2)) then 0=2x-(pi/2) since sin(0)=0 but doen't look it

still don't know how to convert this to latex

K
 
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You're on the right track. Start with y=0 and then like you said use the fact that sin(0)=0. So solve [math]2x-\frac{\pi}{2}=0[/math]. That is only one of possibly infinite intercepts though. For what values of theta, does [math]\sin(\theta)=0[/math]? Not just at 0. How can you generalize these?
 
well i did this 0=2(x-(pi/4)) so from this looks like if x = (pi/4) then the intercepts this plus K(pi/4)+pi ?
 
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Not quite sure I would agree with the solutions so far. $\sin(z)=0$ when $z=n\pi$, for any integer $n$. So, set $2(x-\pi/4)=n\pi$ and solve for $x$. What do you get?
 
I would use Ackbach's method to solve this. We know that $\sin(x) = 0$ when $x = n\pi$ where n is an integer (you can check this by graphing the result and using the periodicity of sin(x) to extend it)
Thus $2\left(x- \frac{\pi}{4}\right) = n\pi \Leftrightarrow x - \frac{\pi}{4} = \frac{n\pi}{2}$

Add $\frac{\pi}{4}$ to both sides to get the general set of solutions.

Typically these questions ask for solutions between $0$ and $2\pi$. If this is the case then $n=0,1,2$

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To render latex, use a single dollar sign at each end of your latex (or a double dollar sign to centre it, again at each end). http://www.mathhelpboards.com/showthread.php?27-How-to-use-LaTeX-on-this-site has more information including how to decode someone else's (although I go with the quote the post and look for myself method :cool:)

Code:
$2\left(x- \frac{\pi}{4}\right) = n\pi \Leftrightarrow x - \frac{\pi}{4} = \frac{n\pi}{2}$
becomes $2\left(x- \frac{\pi}{4}\right) = n\pi \Leftrightarrow x - \frac{\pi}{4} = \frac{n\pi}{2}$
 
Doh! Sorry guys and thanks for catching my mistake. Clearly it's not [math]2 \left(x-\frac{\pi}{4} \right) + n\pi[/math] but when [math]2 \left(x-\frac{\pi}{4} \right) = n\pi[/math]
 
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