Скачать или смотреть [ Pre-Calculus/SAT/AP exam/IB exam ]-Analyzing Cosine Function Parity, Period... [Trigonometry]

This Video (based on our math blog and class recordings) offers a detailed mathematical analysis of the function f(x)=cos⁡(π2−∣x∣)f(x) = \cos\left(\frac{\pi}{2} - |x|\right), which is first simplified using a trigonometric identity to f(x)=sin⁡(∣x∣)f(x) = \sin(|x|). The analysis methodically determines three key properties of the function: its parity, which is found to be even because f(−x)f(-x) equals f(x)f(x); its least positive period, which is determined to be π\pi; and its monotonicity on the interval [0,π2][0, \frac{\pi}{2}], where it is shown to be increasing. The source is structured as a problem-solving guide, complete with step-by-step calculations and a final summary of the results. Additionally, a crucial tip is offered to always simplify the function first to avoid errors in subsequent calculations of its properties.


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