For problems #1-10, graph at least two periods of each function, state the domain, range, amplitude and period, and label the axes accordingly.
1) \(f(x)=\sin x\)
2) \(g(x) = \cos x\)
3) \(h(x)=2\sin x\)
4) \(m(x)=-3\cos x\)
5) \(n(x)=4\cos(x) + 1\)
6) \(p(x)=-2\sin(x) - 3\)
7) \(r(x)=\cos(2x) - 1\)
8) \(s(x)=2\sin (\pi x)\)
9) \(t(x)= \cos\left(\Large\frac{2π}{3}\normalsize x\right)\)
10) \(w(x)= - \sin \left(\Large\frac{\pi}{4} \normalsize x\right) +1\)
For problems #11-20, write a function represented by each graph.
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20) Challenge:
Review
21) Evaluate \(\cos\left(\Large\frac{2π}{3}\right)\).
22) What is the length of an arc that is subtended by an angle of measure \(50 ^{\circ}\) with radius \(4\) feet?
23) Find the sum, \(\sum\limits_{i=1}^{\infty} 4(\frac{1}{3})^{i-1}\).
24) If the half life of a substance is \(3\) days and we began with \(52\) grams of the substance and currently have \(20\) grams, about how old is the substance? Round to the nearest hundredth.
25) Evaluate \(\ln(e^4)\).
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