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.
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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