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Solve for x. 100cos(360 - x) + 150cos(330-x) + 200cos(180 + x) = 0 100cos(x) + 150cos(30 + x ) -200cos(x) =0 I have to find the value of x but i can't get to it. I always get the wrong angle but I can't figure out what to do differently. If you draw the x value on a graph you can see that those two equations are the same exept that i changed the + for a - for the last one since it's going in the negative x. The answer is 21.7 degrees.

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Lix Lemjay eNotes educator | Certified Educator

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To simplify the equation, use the identity for sum and difference of two angles which are:



So the equation becomes,


Note that c`os360=1` , `sin360=0` , `cos330=sqrt3/2` , `sin330=-1/2` , `cos180=-1` and `sin180=1` .



Then, divide both sides by the GCF of the equation.



Combine like terms.


Then express this as one trigonometric function. Divide both sides by cosx.



Note that `tanx =(sinx)/(cosx)` .


Isolate the term with x.





Hence, the value of x in the given equation is `21.7^o` .

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mathieu1881 | Student

Super clear answer, thank you very much. I didn't planned on using trigonometric identities but this was the way to go. You should be a teacher at the university instead of here, your clear explanations would me much appreciated. 5 stars