sinx -xmultiplied by cosx -(pi/2)=0

please note, working in radians

any method to give the solution thats not an approximation

please email with any solutions

thanks

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- May 10th 2008, 02:28 PMLaurenBFind x, anyone help?
sin

**x -****x**multiplied by cos**x -**(pi/2)=0

please note, working in radians

any method to give the solution thats not an approximation

please email with any solutions

thanks - May 10th 2008, 02:48 PMmr fantastic
Well the method I propose uses routine algebra and recognition of special angles and values.

Using the null factor law (you might know it by a different name):

$\displaystyle \sin (x) - x = 0 \Rightarrow \sin x = x$ .... (1)

or

$\displaystyle \cos (x) - \frac{\pi}{2} = 0 \Rightarrow \cos x = \frac{\pi}{2}$ .... (2)

Regarding equation (1), an obvious exact solution is x = 0. The tricky bit is to show that this actually the*only*solution ......

**Edit: Deleted my remarks on equation (2) for reasons made obvious by an ancient Greek philosopher!** - May 10th 2008, 03:29 PMPlato
- May 10th 2008, 03:37 PMmr fantastic