SOLUTION: Given that x is measured in radians and x is greater than 10, find the smallest value of x such that {{{10cos((x+1)/(2)) = 3 }}} *Please answer as soon as possible bro :)

Divide both sides by 10



Use inverse cosine on a calculator to get
the principle value of 1.266103873

That's the 1st quadrant value.  There is also a
4th quadrant answer of -1.266103873.  We will
have to consider both cases.

FIRST QUADRANT value of 

We can add 2pn and get 1st quadrant coterminal 
angles with that.

So we have 



Solve for x:

Multiply through by 2



Subtract 1 from both sides



We set that greater than 10



Solve for n:







The smallest integer value of n is 1. 
So



x = 14.09857796

That may be the answer, but we have 
to consider the 4th quardrant value
as well to be sure.

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FOURTH QUADRANT value of 

We can add 2pn and get 4th quadrant coterminal 
angles with that.

So we have 



Solve for x:

Multiply through by 2



Subtract 1 from both sides



We set that greater than 10



Solve for n:





The smallest integer value of n that satisfies
that is 2.  So



x = 21.60053388
 
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That is larger so the smallest solution for x
that satisfies



and is greater than 10 is 14.09857796.

Edwin