# Find the point on the curve y=cosx closest to the point (0,0)?

##### 1 Answer

The point is

#### Explanation:

By the distance formula, the distance between

#d= sqrt((x -0)^2 + (cosx - 0)^2)#

#d = sqrt(x^2 + cos^2x)#

To find the minimum distance, we need to differentiate.

#d' = (2x - 2cosxsinx)/(2sqrt(x^2 + cos^2x))#

#d' = (x - cosxsinx)/sqrt(x^2 + cos^2x)#

We wish for this to be the smallest possible, thus we need

#0 = (x - cosxsinx)/sqrt(x^2 + cos^2x)#

#0 = x - cosxsinx#

Use a graphing application to solve and find that

There derivative is negative when

Hopefully this helps!