Question 834961: sqrt 2 cos(5x+5)=cot5 then what is the value of x
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i worked in radians.
i tried the same problem using degrees and it didn't worked.
apparently the 5 is in radians since degrees won't work with this problem.
the equation is:
sqrt(2) * cos(5x+5) = cot(5)
i divided both sides of the equation by sqrt(2) to get:
cos(5x+5) = cot(5) / sqrt(2)
i used my calculator to find cot(5) / sqrt(2) and got -.2091713185.
this made my equation becomes:
cos(5x+5) = -.2091713185.
if cos(5x+5) is equal to -.2091713185, then:
5x+5 must be equal to arccos(-.2091713185).
this means i needed to find the angle whose cosine was -.2091713185.
arccos(-.2091713185) is equal to 1.781523782.
this means that:
5x+5 = 1.781523782.
subtract 5 from both sides of this equation and then divide both sides of this equation by 5 and you will get:
x = (1.781523782 - 5) / 5 which becomes:
x = -.6436952436.
all that's required now is to confirm the answer is correct.
this is done by replacing x in the original equation with -.6436952436 and determining if the equation is true.
so that's what i did.
sqrt(2) * cos(5x+5) = cot(5) becomes:
sqrt(2) * -.2091713185 = -.2958129155
simplify this to get:
-.2958129155 = -.2958129155
this confirms the solution is correct.
i then went back and set my calculator to degrees.
when i set my calculator to degrees. i get the following:
cot(5)/sqrt(2) is equal to 8.082267493
my equation becomes:
cos(5x+5) = 8.082267493.
i tried to get the arccos of 8.082267493 and couldn't.
the calculator threw up.
it threw up because the cosine of an angle can never be greater than 1.
this led to my conclusion that you had to be working in radians.
anyway, i did get a good answer using radians and it did confirm to be true so that should be what you need on this one.
the answer is:
x = -.6436952436 which you can round to whatever number you want.
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