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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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` .
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
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