range of sin²x + sin x + 2
In this question, since sine ranges from -1 to 1, I thought that the minimum value would be when sin x gives us 0 (or -1 would work too), then we would get a result of 2. And for maximum, it would be when sin x is 1, so we get 4. So the range should have been [2,4] but this doesn't match any options.
I tried finding online solutions but there are none to this exact problem, and for similar problems, they add and subtract a value so as to form an equation in the form a² + b² + 2ab to take a whole square, I don't understand why would the do that when we know the range of sine already.
I tried finding online solutions but there are none to this exact problem, and for similar problems, they add and subtract a value so as to form an equation in the form a² + b² + 2ab to take a whole square, I don't understand why would the do that when we know the range of sine already.
