Need help with solving equation...

[zivku]

the equation is:

y = 2x - tanx

and i'm finding the x-intercepts, when setting y = 0
0 = 2x - tanx
tanx = 2x

and then i don't know what to do, i know the answers are -3pi/8 and 3pi/8, (i think), but don't know how to get there. all help is appreciated, thanks in advance.

 

[Unco]

G'day, Zivku.

If you sketch a graph of y=2x and of y=tan(x), you can see they intersect at the origin, and then infinitely many times as y=2x crosses the asymptotic y=tan(x) curves. (The x-ordinates of where they intersect are the x-intercepts of y=2x-tan(x).

Have you been provided with an interval to work with? You would then need to use numerical methods (eg. Newton-Raphson) to find the roots . . .

~~~~~~~~~~~~~~~~~~~~~~~~~~~

Do you get zero if you plug x=3pi/8 into 2x-tan(x)? If so, a firm letter should be sent to your calculator's manufacturer!