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I just want to check my work because I have no idea if I am doing this right:

The equation I am given is sin(3x) = 0.34.

I am supposed to find all values of x in degrees that satisfy the equation above and round approximate answers to the nearest tenth of a degree.

 

My answer:

Sin(3x) = 0.34

3x = sin^-1(0.34) = 19.9 degrees 

OR 180 - 19.9 = 160.1 degrees

x = 6.6 degrees or x = 53.4 degrees (after dividing 3x by 3)

 

The solution set is {6.6 degrees, 53.4 degrees}

 

Is this correct?

 Apr 27, 2019
edited by Guest  Apr 27, 2019
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sin (3x)  = 0.34 

 

sin (x) = 0.34   at 19.9°    and at  [180 - 19.9]° =  160.1°

 

So  we get  19.9° + 2pi*n      and    160.1° + 2pi * n

 

So...dividing these by 3, we get  6.6° + (2/3)pi*n    and 53.4° +(2/3)pi* n   as general solutions

 

 

cool cool cool

 Apr 27, 2019

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