SOLUTION: solve the equation for x, where o<=x<=360. sin(3x)+ 2=1.5

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Question 1071446: solve the equation for x, where o<=x<=360.
sin(3x)+ 2=1.5

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
sin%283x%29%2B2-2=1.5-2
sin%283x%29=-1%2F2
That sine means angle points into Q3 or Q4. (Refer to the Unit Circle.)

Your common reference angle is 30 degrees, but since the sine indicates Q3 or Q4, also refer to how this relates to 180 degrees and to 360 degrees.

system%28cross%283x=120%29%2C3x=210%2Cor%2C3x=330%29, measure is degrees.
(fixed small mental visualization mistake)


ANSWER:
system%28x=70%2Adegrees%2C+or%2C+x=110%2Adegrees%29

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
solve the equation for x, where o<=x<=360.
sin(3x)+ 2=1.5
~~~~~~~~~~~~~~~~~~~~~~

sin(3x) + 2 = 1.5  --->

sin(3x) = -0.5  --->


3x = 210°  or/and  3x = 330°.

--->  x = 70°  or/and  x = 110°.


But also  

1)  3x = 210+ 360° = 570°  or/and  3x = 330° + 360° = 690°,   which gives 

    x = 570%2F3 = 190°   or/and  x = 690%2F3 = 230°.


and


2)  3x = 210+ 720° = 930°  or/and  3x = 330° + 720° = 1050°,   which gives 

    x = 930%2F3 = 310°   or/and  x = 1050%2F3 = 350°.


Answer.   The solutions are 70°,  110°,  190°,  230°,  310°  and 350°.




Plot y = sin(3x)  (red)  and  y = -1%2F2  (green)


The solution by "josgarithmetic" is   W R O N G.


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"josgarithmetic",  you are mathematically illiterate person.

I prove it to you and to all others in this site just hundreds of times.

What are you doing in this forum   ? ?

Do not shame this forum  ! ! !

OK,  I know what you can do here:  the problems on the slope,  intercepts . . .
        What else ???

You absolutely do not fit as a tutor neither for word problems, nor for trigonometry.

Please do not touch that areas and that problems where you are not competent !


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