Question

Оцените значение выражения: − 4 + 3 sin2α.

Answer 1

sin2α изменяется в пределах [-1;1]. Будем оценивать в виде двойного неравенства:

$-1\leqslant \sin2\alpha\leqslant1~~|\cdot 3\\ \\ -3\leqslant3\sin2\alpha\leqslant3~~~|-4\\ \\ -7\leqslant-4+3\sin2\alpha\leqslant-1$

Значение выражения -4+3sin2α есть [-7;-1]

Answer 2

To evaluate the expression −4 + 3sin^2(α), we need to know the value of the angle α. Since you haven't provided a specific value for α, I can only give you the general expression:

−4 + 3sin^2(α)

The value of sin^2(α) can vary between 0 and 1 because it's the square of the sine function. When sin^2(α) is at its maximum value of 1, the expression becomes:

−4 + 3(1) = −4 + 3 = -1

And when sin^2(α) is at its minimum value of 0, the expression becomes:

−4 + 3(0) = −4 + 0 = -4

Without a specific value for α, we can't provide a definitive numerical answer. But we know that the result will always lie between -4 and -1.