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Magazine Problem 8
A note on the piano has given frequency \(F\). Suppose the maximum displacement at the center of the piano wire is given by \(s(0) .\) Find constants a and \(\omega\) so that the equation $$s(t)=a \cos \omega t$$ models this displacement. Graph s in the viewing window \([0,0.05]\) by \([-0.3,0.3].\) $$F=220 ; s(0)=0.06$$
Problem 13
The graphs of \(y=\sin x+1\) and \(y=\sin (x+1)\) are \(\mathrm{NOT}\) the same. Explain why this is so.
Problem 18
Graph each function over a one-period interval. $$y=2+\frac{1}{4} \sec \left(\frac{1}{2} x-\pi\right)$$
Problem 19
A weight attached to a spring is pulled down 3 in. below the equilibrium position. (a) Assuming that the frequency is \(\frac{6}{\pi}\) cycles per sec, determine a model that gives the position of the weight at time \(t\) seconds. (b) What is the period?
Problem 28
Give a short explanation Explain why an angle of radian measure \(t\) in standard position intercepts an arc of length \(t\) on a circle of radius 1
Problem 28
Find a calculator approximation for each circular function value. $$\tan 6.4752$$
Problem 32
Convert each radian measure to degrees. $$\frac{2 \pi}{3}$$
Problem 39
$$\text {Graph each function over a two-period interval. Give the period and amplitude.}$$ $$y=\pi \sin \pi x$$
Problem 46
Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that \(\pi \approx 3.14 .)\) $$\sin (-1)$$
Problem 46
Graph each function over a two-period interval. $$y=2-3 \cos x$$
