جواب تمرین صفحه ۳۳ حسابان (2)

الف) \(y = 1 + 2\sin 7x\)

\(\max = |2| + 1 = 3\)، \(\min = -|2| + 1 = -1\)، \(T = \dfrac{2\pi}{|b|} = \dfrac{2\pi}{7}\)

ب) \(y = \sqrt{3} - \cos\dfrac{\pi}{2}x\)

\(a = -1\)، \(c = \sqrt{3}\)

\(\max = |-1| + \sqrt{3} = 1 + \sqrt{3}\)، \(\min = -|-1| + \sqrt{3} = \sqrt{3} - 1\)، \(T = \dfrac{2\pi}{\frac{\pi}{2}} = 4\)

پ) \(y = -\pi\sin\left(\dfrac{x}{2}\right) - 2\)

\(a = -\pi\)، \(c = -2\)

\(\max = |\pi| - 2 = \pi - 2\)، \(\min = -|\pi| - 2 = -\pi - 2\)، \(T = \dfrac{2\pi}{\left|\frac{1}{2}\right|} = 4\pi\)

ت) \(y = -\dfrac{3}{4}\cos 3x\)

\(\max = \left|-\dfrac{3}{4}\right| = \dfrac{3}{4}\)، \(\min = -\left|-\dfrac{3}{4}\right| = -\dfrac{3}{4}\)، \(T = \dfrac{2\pi}{3}\)