SOLUTION: cosx = x/2 Is it possible to evaluate the above with proper mathematical solution? If yes, show workings. Thanx in advance.

Algebra ->  Finance -> SOLUTION: cosx = x/2 Is it possible to evaluate the above with proper mathematical solution? If yes, show workings. Thanx in advance.      Log On


   



Question 1091702: cosx = x/2
Is it possible to evaluate the above with proper mathematical solution?
If yes, show workings.
Thanx in advance.

Found 2 solutions by Edwin McCravy, math_helper:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
On the left side, the variable x appears as part of a trigonometric
function, the cosine.  But on the right side, the variable x does NOT
appear as part of a trigonometric function.

When an equation is such that the variable x appears 
both within a trigonometric function and also outside 
a trigonometric function, there is no way to solve the
equation using algebra or special angles.  All we can do
is approximate the answer using a graphing calculator.
This is beyond the limits of ordinary algebra and 
trigonometry.

The approximate answer is x = 1.0298665 radians, (not degrees),
but it is only possible to get such approximate answers when
the variable appears as part of a trigonometric function and
also NOT as part of a trigonometric function using technology,
such as a TI-83 or TI-84, or some computer application.  It
can also be done by trial and error, but not algebra.

Edwin

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
I agree with the other tutor. Just want to add that sometimes plotting the function helps you get a quick estimate of the solution. To do that, you'd write +f%28x%29+=+cos%28x%29+-+x%2F2+, then plot f(x) and see where f(x) = 0:

+graph%28300%2C300%2C+-10%2C10%2C-10%2C10%2Ccos%28x%29-x%2F2%29+

Zooming in on the region near x=1:
+graph%28400%2C400%2C-1%2C2%2C-1.5%2C1.5%2Ccos%28x%29-x%2F2%29+