Find the smallest function value y = sin ^ 2x + sinx +1

Because the function y = sin x is defined on the interval [-1; 1], then in order to calculate the smallest value of the original function, it is enough to consider three cases:

1.sin x = -1, then the original function y = 1 – 1 + 1 = 1.

2.sin x = 1, then we get that y = 1 + 1 + 1 = 3.

3.sin x = 0, therefore, we have y = 0 + 0 + 1 = 1.

We got that the smallest value of the function is 1.

Answer: the minimum value of the function is 1.