(a) find the minimum value and the maximum value,
(b) find the period.
Solutions: (a) min. value: \(-1\), max. value: \(1\); (b) period: \(360^\circ\)(a) find the minimum value and the maximum value,
(b) find the period.
Solutions: (a) min. value: \(-2\), max. value: \(2\); (b) period: \(360^\circ\)(a) find the amplitude,
(b) find the principal axis,
(c) find the minimum value and the maximum value,
(d) find the period.
Solutions: (a) amplitude: \(2\); (b) principal axis: \(y=1\); (c) min. value: \(-1\), max. value: \(3\); (d) period: \(360^\circ\)(a) find the minimum value and the maximum value,
(b) find the period.
Solutions: (a) min. value: \(-1\), max. value: \(1\); (b) period: \(120^\circ\)(a) find the minimum value and the maximum value,
(b) find the period.
Solutions: (a) min. value: \(-1\), max. value: \(1\); (b) period: \(360^\circ\)(a) find the minimum value and the maximum value,
(b) find the period.
Solutions: (a) min. value: \(-1\), max. value: \(1\); (b) period: \(180^\circ\)(a) find the minimum value and the maximum value,
(b) find the period.
Solutions: (a) min. value: \(-1\), max. value: \(1\); (b) period: \(360^\circ\)(a) find the principal axis,
(b) write down the range,
(c) find all minima for \(0^\circ\leqslant x\leqslant 360^\circ\).
Solutions: (a) principal axis: \(y=1\); (b) range: \(-2\leqslant y \leqslant 4\); (c) minimum at: \((180^\circ,-2)\)(a) find all \(x\)-intercepts for \(0^\circ\leqslant x\leqslant 360^\circ\),
(b) write down minima and maxima for \(0^\circ\leqslant x\leqslant 360^\circ\).
Solutions: (a) \(x\)-intercepts: \(30^\circ,~90^\circ,~150^\circ,~210^\circ,~270^\circ,~330^\circ\); (b) min.: \((60^\circ,-1),~(180^\circ,-1),~(300^\circ,-1)\), max.:\((0^\circ,1),~(120^\circ,1),~(240^\circ,1),~(360^\circ,1)\)(a) find \(y\)-intercept,
(b) find all \(x\)-intercepts on \([0,360^\circ]\),
(c) write down the greatest and the least value, and state the smallest non-negative value of \(x\) for which they occur.
Solutions: (a) \(y\)-intercept: \(2\sqrt{3}\); (b) \(x\)-intercepts: \(120^\circ,~ 300^\circ\); (c) min. value \(-4\) occurs at \(x=210^\circ\), max. value \(4\) occurs at \(x=30^\circ\)(a) find the principal axis, amplitude and period,
(b) write the function in the form \(y=A\sin x +D\)
(a) find the principal axis, amplitude and period,
(b) write the function in the form \(y=A\sin Bx +D\)
(a) find the minimum value and the maximum value,
(b) find the period.
Solutions: (a) min. value: \(-1\), max. value: \(1\); (b) period: \(2\pi\) radians(a) find the minimum value and the maximum value,
(b) find the period.
Solutions: (a) min. value: \(-1\), max. value: \(1\); (b) period: \(2\pi\) radians(a) find the principal axis,
(b) find the minimum value and the maximum value,
(c) find the period.
Solutions: (a) principal axis: \(y=1\); (b) min. value: \(-1\), max. value: \(3\); (c) period: \(2\pi\)(a) find the domain and range,
(b) find the period,
(c) write down minima and maxima.
Solutions: (a) domain: \(\mathbb{R}\), range: \([2,4]\); (b) period: \(\pi\); (c) min.: \((-\frac{\pi}{4}+k\pi,2)\), max.:\((\frac{\pi}{4}+k\pi,4),~~ k\in\mathbb{Z}\)(a) find all \(x\)-intercepts on \(0\leqslant x\leqslant 2\pi\),
(b) write down minima and maxima on \(0\leqslant x\leqslant 2\pi\).
Solutions: (a) \(x\)-intercepts: \(\frac{\pi}{6},~\frac{\pi}{2},~\frac{5\pi}{6},~\frac{7\pi}{6},~\frac{3\pi}{2},~\frac{11\pi}{6}\); (b) min.: \((\frac{\pi}{3},-1),~(\pi,-1),~(\frac{5\pi}{3},-1)\), max.:\((0,1),~(\frac{2\pi}{3},1),~(\frac{4\pi}{3},1),~(2\pi,1)\)(a) find \(y\)-intercept,
(b) find all \(x\)-intercepts on \([0,2\pi]\),
(c) write down the greatest and the least value, and state the smallest non-negative value of \(x\) for which they occur.
Solutions: (a) \(y\)-intercept: \(2\sqrt{3}\); (b) \(x\)-intercepts: \(\frac{2\pi}{3},~ \frac{5\pi}{3}\); (c) min. value \(-4\) occurs at \(x=\frac{7\pi}{6}\), max. value \(4\) occurs at \(x=\frac{\pi}{6}\)