Question

In Exercises 17–24, graph two periods of the given cotangent function. y = 2 cot x

Accepted Answer

Recall that the cotangent function $$ \cot x $$ has a period of $$ \pi . $$Since the function is $$ y = 2 \cot x $$, the period remains $$ \pi $$ because the coefficient 2 only affects the amplitude, not the period. Determine the interval for two periods. Since one period is $$ \pi $$, two periods will span an interval of $$ 2\pi . $$For example, you can graph from $$ x = 0  to$$ $$ x = 2\pi . $$Identify the key points within one period where the cotangent function has vertical asymptotes and zeros. The cotangent function has vertical asymptotes where $$ \sin x = 0 $$, i.e., at $$ x = 0, \pi, 2\pi, \ldots $$, and zeros where $$ \cos x = 0 $$, i.e., at $$ x = \frac{\pi}{2}, \frac{3\pi}{2}, \ldots . $$Calculate the corresponding $$ y -$$values for the function $$ y = 2 \cot x  at $$points between the asymptotes, using the formula $$ y = 2 \cot x = 2 \frac{\cos x}{\sin x} . $$This will help you plot the shape of the graph accurately. Sketch the graph by drawing vertical asymptotes at $$ x = 0, \pi, 2\pi $$, plotting the calculated points, and drawing the cotangent curve between these asymptotes for two full periods.

In Exercises 17–24, graph two periods of the given cotangent function. y = 2 cot x

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Cotangent Function and Its Properties

Amplitude and Vertical Stretch

Period of the Cotangent Function