# How do I find the frequency of a sinusoidal graph?

In a sinusoidal model of the form y = $a \cdot \sin \left(b \left(x - c\right)\right) + d$, the period is found by taking $\frac{2 \cdot \pi}{|} b |$. Frequency is the reciprocal of period.
Example: y = $2 \cdot \sin \left(3 x\right)$ would have a period of $\frac{2 \pi}{3}$, which is one-third the length of the "normal" period of $2 \pi$. Another way to describe this change from the Parent function would be to say that the graph would cycle through 3 times by the time it reaches $2 \pi$. The frequency looks like it is directly affected by the value of "b" in this equation, which is 3.
Now, make a prediction yourself. What is the frequency of the graph of y = $- \frac{1}{4} \cdot \sin \left(\left(\frac{1}{2}\right) x\right) + 1$?
Answer: The period would be $\frac{2 \pi}{\frac{1}{2}}$ or $4 \pi$, which is twice as long as the Parent function. The frequency would be $\frac{1}{4 \pi}$, which is difficult to interpret. If the period is DOUBLED, then the frequency is cut in half. You will only see HALF of a cycle by the time you reach $2 \pi$ in this case.