Chapter 1: Problem 16
In Exercises \(13-16,\) write the point-slope equation for the line through the point \(P\) with slope \(m .\) $$P(-4,0), \quad m=-2$$
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Exploration Let y=\sin (a x)+\cos (a x) Use the symbolic manipulator of a computer algebra system (CAS) to help you with the following: (a) Express \(y\) as a sinusoid for \(a=2,3,4,\) and 5 (b) Conjecture another formula for \(y\) for \(a\) equal to any positive integer \(n .\) (c) Check your conjecture with a CAS. (d) Use the formula for the sine of the sum of two angles (see Exercise 56 \(\mathrm{c}\) ) to confirm your conjecture.
In Exercises 59 and \(60,\) show that the function is periodic and find its period. $$f(x)=\cos (60 \pi x)$$
Finding the Period Give a convincing argument that the period of tan \(x\) is \(\pi .\)
In Exercises \(39-42,\) draw the graph and determine the domain and range of the function. $$y=\log _{2}(x+1)$$
Tripling Your Money Determine how much time is required for an investment to triple in value if interest is earned at the rate of 5.75\(\%\) compounded daily.
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