### Instructions for Drawing and Labeling a Graph of the Cosine Function1. **Drawing the Axes:** - Use a straightedge to draw the x-axis and the y-axis intersecting at the origin (0,0).2. **Labeling the Axes:** - **Y-Axis:** Label the numbers -1 and 1 on the y-axis. This will represent the range of the cosine function. - **X-Axis:** Label the points spaced equally between integer multiples of $ \frac{\pi}{2} $ over the interval $[-2\pi, 3\pi]$. - Specifically, label the points: $-2\pi$, $-\frac{3\pi}{2}$, $-\pi$, $-\frac{\pi}{2}$, $0$, $\frac{\pi}{2}$, $\pi$, $\frac{3\pi}{2}$, $2\pi$, $\frac{5\pi}{2}$, and $3\pi$.3. **Graphing the Function $ y = \cos x $:** - Plot the graph of the cosine function $ y = \cos x $ over the given interval $[-2\pi, 3\pi]$. - **Key Points to Plot:** - $ (0, 1) $ - $ (\pm\frac{\pi}{2}, 0) $ - $ (\pm\pi, -1) $ - $ (\pm\frac{3\pi}{2}, 0) $ - $ (\pm2\pi, 1) $ - Continue this pattern until reaching $3\pi$.4. **Connecting the Points:** - Draw a smooth, continuous curve through these points to represent the cosine wave.By following these instructions, you will create an accurate graph of the cosine function $ y = \cos x $ over the specified interval.

Cosine function has period of , and it achieves it max values at . Max value for cosine function…

2. Use a straightedge to draw the x- and y-axis. Label the numbers -1 and 1 on the y-axis. On the x-axis label the points spaced equally between integer multiples of 5 over the interval [-2 7, 3 ]. Graph the function y = cos x.

2. Use a straightedge to draw the x- and y-axis. Label the numbers -1 and 1 on the y-axis. On the x-axis label the points spaced equally between integer multiples of 5 over the interval [-2 7, 3 ]. Graph the function y = cos x.

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

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### Instructions for Drawing and Labeling a Graph of the Cosine Function

1. **Drawing the Axes:**
- Use a straightedge to draw the x-axis and the y-axis intersecting at the origin (0,0).

2. **Labeling the Axes:**
- **Y-Axis:** Label the numbers -1 and 1 on the y-axis. This will represent the range of the cosine function.
- **X-Axis:** Label the points spaced equally between integer multiples of $ \frac{\pi}{2} $ over the interval $[-2\pi, 3\pi]$.
- Specifically, label the points: $-2\pi$, $-\frac{3\pi}{2}$, $-\pi$, $-\frac{\pi}{2}$, $0$, $\frac{\pi}{2}$, $\pi$, $\frac{3\pi}{2}$, $2\pi$, $\frac{5\pi}{2}$, and $3\pi$.

3. **Graphing the Function $ y = \cos x $:**
- Plot the graph of the cosine function $ y = \cos x $ over the given interval $[-2\pi, 3\pi]$.
- **Key Points to Plot:**
- $ (0, 1) $
- $ (\pm\frac{\pi}{2}, 0) $
- $ (\pm\pi, -1) $
- $ (\pm\frac{3\pi}{2}, 0) $
- $ (\pm2\pi, 1) $
- Continue this pattern until reaching $3\pi$.

4. **Connecting the Points:**
- Draw a smooth, continuous curve through these points to represent the cosine wave.

By following these instructions, you will create an accurate graph of the cosine function $ y = \cos x $ over the specified interval.

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