AP Precalculus Quiz
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TRIGONOMETRIC AND POLAR FUNCTIONS
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A rotating beacon's brightness is f(t)=6sin⁡ ⁣(π4t−π6)f(t)=6\sin\!\left(\frac{\pi}{4}t-\frac{\pi}{6}\right) (lumens), with tt in seconds. Using t=θt=\theta, an equivalent polar form is r=6sin⁡ ⁣(π4θ−π6)r=6\sin\!\left(\frac{\pi}{4}\theta-\frac{\pi}{6}\right). On a coordinate plane, the sinusoid has amplitude 66, period 88, and is shifted right by 23\frac{2}{3} seconds from sin⁡ ⁣(π4t)\sin\!\left(\frac{\pi}{4}t\right). This periodicity matches a steady rotating light. Refer to the passage above. Identify the period of the trigonometric function in the graphical representation.​
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