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y = 6 sinx y=6 cos x

y = 6 sinx y=6 cos x

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I fond the area as 16 is that right or no?

**Trigonometric Function Graphs** This diagram shows the graphs of two trigonometric functions, \( y = 6 \sin x \) and \( y = 6 \cos x \), plotted on a coordinate plane. - **Axes:** - The horizontal axis is labeled as \( x \). - The vertical axis is labeled as \( y \). - **Function \( y = 6 \sin x \):** - This function is represented by a blue curve. - It starts at the origin \((0, 0)\), rises to a maximum of 6 at \(\frac{\pi}{2}\), and intersects the horizontal axis again at \( \pi \). - **Function \( y = 6 \cos x \):** - This function is represented by a red curve. - It starts at the maximum value of 6 at \( x = 0 \), decreases to 0 at \(\frac{\pi}{2}\), and continues to decrease below the x-axis beyond the image frame. - **Shaded Region:** - There is a shaded triangular area between the two curves from \( x = 0 \) to \( x = \frac{\pi}{2} \). This region indicates the area where the graph of \( y = 6 \cos x \) is above the graph of \( y = 6 \sin x \). This visual representation helps explain the behavior and intersections of the sine and cosine functions within the range from 0 to \( \frac{\pi}{2} \), showcasing their amplitude differences and phase relationships.
Transcribed Image Text:**Trigonometric Function Graphs** This diagram shows the graphs of two trigonometric functions, \( y = 6 \sin x \) and \( y = 6 \cos x \), plotted on a coordinate plane. - **Axes:** - The horizontal axis is labeled as \( x \). - The vertical axis is labeled as \( y \). - **Function \( y = 6 \sin x \):** - This function is represented by a blue curve. - It starts at the origin \((0, 0)\), rises to a maximum of 6 at \(\frac{\pi}{2}\), and intersects the horizontal axis again at \( \pi \). - **Function \( y = 6 \cos x \):** - This function is represented by a red curve. - It starts at the maximum value of 6 at \( x = 0 \), decreases to 0 at \(\frac{\pi}{2}\), and continues to decrease below the x-axis beyond the image frame. - **Shaded Region:** - There is a shaded triangular area between the two curves from \( x = 0 \) to \( x = \frac{\pi}{2} \). This region indicates the area where the graph of \( y = 6 \cos x \) is above the graph of \( y = 6 \sin x \). This visual representation helps explain the behavior and intersections of the sine and cosine functions within the range from 0 to \( \frac{\pi}{2} \), showcasing their amplitude differences and phase relationships.
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