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Use a calculator to solve the equation on the interval [0, 2π). Round to the nearest hundredth of a radian. sin 2x - sin x = 0

 Feb 6, 2016

Best Answer 

 #1
avatar+129258 
+10

We don't really need a calculator, here...

 

Note, sin2x  = 2sinxcosx.......so we have....

 

2sinxcox - sinx  = 0       factor out sinx

 

sinx (2cosx - 1)  =  0

 

So, setting each factor to 0, we have that  

 

sinx = 0      and this happens at 0 radians and pi radians on the interval  ....or....

 

2cosx - 1  = 0       add 1 to both sides

 

2cosx  = 1        divide both sides by 2

 

cosx  =  1/2       and this happens at pi/3  radians and 5pi/3  radians  on the interval

 

[ These solutions are exact values....]

 

 

cool cool cool

 Feb 6, 2016
 #1
avatar+129258 
+10
Best Answer

We don't really need a calculator, here...

 

Note, sin2x  = 2sinxcosx.......so we have....

 

2sinxcox - sinx  = 0       factor out sinx

 

sinx (2cosx - 1)  =  0

 

So, setting each factor to 0, we have that  

 

sinx = 0      and this happens at 0 radians and pi radians on the interval  ....or....

 

2cosx - 1  = 0       add 1 to both sides

 

2cosx  = 1        divide both sides by 2

 

cosx  =  1/2       and this happens at pi/3  radians and 5pi/3  radians  on the interval

 

[ These solutions are exact values....]

 

 

cool cool cool

CPhill Feb 6, 2016

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