(a) Show that a root of $\sin (x) − x/5 = 0$ lies between $x = 2$ and $x = 3$.
(b) Use the method of halving the interval twice to find an estimate of the root.
I tried to do $f(x)=\sin(2)-2/54$, but I got $-0.3651005033$
The answers has $ 0.51 $?
Once I know how to do part (a), I can do part (b).
Thank you in advance!!
If you got -0.36 but the answer is supposed to have 0.51, then you probably have the wrong mode in your calculator. Check if the answer is supposed to be in degrees or radians and if your calculator is in the same mode as your answer is supposed to be in. To help you with a, to show that a root exists between x = 2 and x = 3, plug in those values into the function. Since the function is continuous between those x-values, you can use the Intermediate Value Theorem to show that a root exists between those two x-values.
Edit: From NoChance's comment, here is a link to the theorem I referenced if you want more information: https://en.wikipedia.org/wiki/Intermediate_value_theorem