Question

Explain why the equation `sintheta=0` has no solution in the interval `(pi,2pi)`?

Answer 1

Pleasesee below.

Explanation:

When you write the interval as `(pi,2pi)`, this means that all real numbers between `pi` and `2pi` are included, but not `pi` and `2pi` themselves.

Now we have `sinpi=0` and also `sin2pi=0`, but for no value between `pi` and `2pi`, we have its Sine ratio as zero.

Hence as `pi` and `2pi` are not included in `(pi,2pi)`, `sintheta=0` does not have any solution in the interval `(pi,2pi)`.