91Ó°ÊÓ

Why are the sine and cosine functions called periodic functions?

How does the graph of \(y=\sin x\) compare with the graph of \(y=\cos x ?\) Explain how you could horizontally translate the graph of \(y=\sin x\) to obtain \(y=\cos x .\)

For the equation \(A \cos (B x+C)+D,\) what constants affect the range of the function and how affect the range?

How does the range of a translated sine function relate to the equation \(y=A \sin (B x+C)+D ?\)

How can the unit circle be used to construct the graph of \(f(t)=\sin t ?\)

For the following exercises, graph two full periods of each function and state the amplitude, period, and midine. State the maximum and minimum \(y\) -values and their corresponding \(x\) -values on one period for \(x>0 .\) Round answers to two decimal places if necessary. $$ f(x)=2 \sin x $$

For the following exercises, graph two full periods of each function and state the amplitude, period, and midine. State the maximum and minimum \(y\) -values and their corresponding \(x\) -values on one period for \(x>0 .\) Round answers to two decimal places if necessary. $$ f(x)=\frac{2}{3} \cos x $$

For the following exercises, graph two full periods of each function and state the amplitude, period, and midine. State the maximum and minimum \(y\) -values and their corresponding \(x\) -values on one period for \(x>0 .\) Round answers to two decimal places if necessary. $$ f(x)=-3 \sin x $$

For the following exercises, graph two full periods of each function and state the amplitude, period, and midine. State the maximum and minimum \(y\) -values and their corresponding \(x\) -values on one period for \(x>0 .\) Round answers to two decimal places if necessary. $$ f(x)=4 \sin x $$

For the following exercises, graph two full periods of each function and state the amplitude, period, and midine. State the maximum and minimum \(y\) -values and their corresponding \(x\) -values on one period for \(x>0 .\) Round answers to two decimal places if necessary. $$ f(x)=2 \cos x $$