Graphing Parametric Functions - SAT Subject Test in Math II

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Question

Give the period of the graph of the equation

$f(x) = \frac{4}{7} \cos \left ( \frac{3\pi x}{7} \right )$

Answer

The period of the graph of a cosine function $f(x)= A \cos Nx$ is $\frac{2 \pi}{N}$ , or $2 \pi \div N$

Since $N = \frac{3\pi}{7}$ , the period is

$2 \pi \div \frac{3\pi}{7} = \frac{2 \pi }{1}\times \frac{7} {3\pi}= \frac{14}{3}$

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