+0  
 
0
651
4
avatar

solve sin (pi/4(x-6))=0.5 algebraically

Guest Jun 7, 2015

Best Answer 

 #1
avatar+78577 
+10

If we just restrict ourselves to [0, 2pi], the sine will equal .5 at  pi/6 and 5p/6 rads

 

So we have....   (pi/4(x-6))= pi/6  →  pi/4 *x - 3pi/2  = pi/6  →    pi/4 * x  =  [5pi/3]/   →  x = [5pi/3][4/pi]

→  20/3

 

Also ....   (pi/4(x-6)) = 5pi/6 →  pi/4 *x - 3pi/2  = 5pi/6  → pi/4 * x = [7 pi/3] →  x = [7pi/3][4/pi]  →  28/3

 

 

CPhill  Jun 7, 2015
Sort: 

4+0 Answers

 #1
avatar+78577 
+10
Best Answer

If we just restrict ourselves to [0, 2pi], the sine will equal .5 at  pi/6 and 5p/6 rads

 

So we have....   (pi/4(x-6))= pi/6  →  pi/4 *x - 3pi/2  = pi/6  →    pi/4 * x  =  [5pi/3]/   →  x = [5pi/3][4/pi]

→  20/3

 

Also ....   (pi/4(x-6)) = 5pi/6 →  pi/4 *x - 3pi/2  = 5pi/6  → pi/4 * x = [7 pi/3] →  x = [7pi/3][4/pi]  →  28/3

 

 

CPhill  Jun 7, 2015
 #2
avatar
+5

what about domain 0<x<2pi??

Guest Jun 22, 2015
 #3
avatar+90994 
+5

 

$$\begin{array}{rlll}
sin (\frac{\pi(x-6)}{4})&=&0.5\\\\
\frac{\pi(x-6)}{4}&=&n\pi +(-1)^n\times \frac{\pi}{6}\qquad & n\in Z\\\\
x-6&=&4n +(-1)^n\times \frac{4}{6}\qquad & n\in Z\\\\
x&=&4n+6 +(-1)^n\times \frac{2}{3}\qquad & n\in Z\\\\
x&=&4n+6 + \frac{(-1)^n\times 2}{3}\qquad & n\in Z\\\\
\end{array}$$

 

I guess that is the domain since that is all the values that x can be  :/

Melody  Jun 22, 2015
 #4
avatar
+5

thank you so much guys, i really appreciate it

Guest Jun 23, 2015

3 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details