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Magazine Problem 18
Identify the period for each of the following. Do not sketch the graph. \(y=\csc \left(\frac{\pi}{3} x\right)\)
Problem 18
Make a table of values for Problems 13 through 18 using multiples of \(\pi / 4\) for \(x\). Then use the entries in the table to sketch the graph of each function for \(x\) between 0 and \(2 \pi\). $$y=\sec x$$
Problem 19
Graph one complete cycle of each of the following. In each case, label the axes accurately and identify the amplitude, period, and vertical translation for each graph. $$ y=-2+2 \sin 4 x $$
Problem 19
Identify the period for each of the following. Do not sketch the graph. \(y=\sec \left(\frac{1}{6} x\right)\)
Problem 19
Make a table using multiples of \(\pi / 4\) for \(x\) to sketch the graph of \(y=\sin 2 x\) from \(x=0\) to \(x=2 \pi\). After you have obtained the graph, state the number of complete cycles your graph goes through between 0 and \(2 \pi\).
Problem 19
Evaluate each expression without using a calculator, and write your answers in radians. $$\cos ^{-1}(-1)$$
Problem 20
Identify the period for each of the following. Do not sketch the graph. \(y=\cot \left(\frac{1}{2} x\right)\)
Problem 20
Graph one complete cycle of each of the following. In each case, label the axes accurately and identify the amplitude, period, and vertical translation for each graph. $$ y=1+\frac{1}{2} \sin 3 x $$
Problem 20
Make a table using multiples of \(\pi / 6\) for \(x\) to sketch the graph of \(y=\sin 3 x\) from \(x=0\) to \(x=2 \pi\). After you have obtained the graph, state the number of complete cycles your graph goes through between 0 and \(2 \pi\).
Problem 20
Evaluate each expression without using a calculator, and write your answers in radians. $$\sin ^{-1}(0)$$
