graphing calculator is recommended. rectangular beam is to be cut from a cylindrical log of diameter d = 20 cm. The figures show different ways this can be done. depth (a) Express the cross-sectional area of the beam as a function of the angle in the figures. A(0) = 400 sin(0)cos (0) (b) Graph the function you found in part (a). A(0) 300 250 200 150 100 50 O width- A(0) 300 250 200 150 100 50 0.5 cm 0.5 1.0 1.0 1.5 1.5 6 8 A(0) 300 250 200 150 100 50 A(0) 20 15 10 5 0.5 0.5 1.0 1.0 (c) Find the dimensions of the beam with largest cross-sectional area. (Round your answers to two decimal places.) width cm depth 1.5 1.5 8 8

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°.
icon
Related questions
Question
how do I approach part c)
The problem involves determining how to cut a rectangular beam from a cylindrical log with a diameter of \( d = 20 \) cm. The challenge is to express and graph the cross-sectional area as a function of the angle \( \theta \).

### (a) Express the Cross-Sectional Area

The problem requires expressing the cross-sectional area \( A(\theta) \) of the beam as a function of the angle \( \theta \):
\[ A(\theta) = 400 \sin(\theta) \cos(\theta) \]

### (b) Graph the Function

Four graphs are presented, showing \( A(\theta) \) as a function of \( \theta \):

1. **Top Left Graph:** A plot of \( A(\theta) \) versus \( \theta \) showing a peak at approximately 1.0 radians, with values on the vertical axis ranging from 0 to 300.
2. **Top Right Graph:** A decreasing curve starting at around 300 and approaching zero as \( \theta \) increases.
3. **Bottom Left Graph:** An increasing graph starting from zero and rising steeply.
4. **Bottom Right Graph:** A plot similar in shape to the top left graph, but with smaller scale on the vertical axis, ranging from 0 to 20.

### (c) Dimensions of the Beam with Largest Cross-Sectional Area

Calculate the dimensions of the beam (width and depth) that result in the largest cross-sectional area. Answers should be rounded to two decimal places.

#### Note

- Users are encouraged to use a graphing calculator to better visualize and verify the functions.
- Two interactive options at the bottom, "Read It" and "Watch It", are likely resources for additional help.
Transcribed Image Text:The problem involves determining how to cut a rectangular beam from a cylindrical log with a diameter of \( d = 20 \) cm. The challenge is to express and graph the cross-sectional area as a function of the angle \( \theta \). ### (a) Express the Cross-Sectional Area The problem requires expressing the cross-sectional area \( A(\theta) \) of the beam as a function of the angle \( \theta \): \[ A(\theta) = 400 \sin(\theta) \cos(\theta) \] ### (b) Graph the Function Four graphs are presented, showing \( A(\theta) \) as a function of \( \theta \): 1. **Top Left Graph:** A plot of \( A(\theta) \) versus \( \theta \) showing a peak at approximately 1.0 radians, with values on the vertical axis ranging from 0 to 300. 2. **Top Right Graph:** A decreasing curve starting at around 300 and approaching zero as \( \theta \) increases. 3. **Bottom Left Graph:** An increasing graph starting from zero and rising steeply. 4. **Bottom Right Graph:** A plot similar in shape to the top left graph, but with smaller scale on the vertical axis, ranging from 0 to 20. ### (c) Dimensions of the Beam with Largest Cross-Sectional Area Calculate the dimensions of the beam (width and depth) that result in the largest cross-sectional area. Answers should be rounded to two decimal places. #### Note - Users are encouraged to use a graphing calculator to better visualize and verify the functions. - Two interactive options at the bottom, "Read It" and "Watch It", are likely resources for additional help.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 14 images

Blurred answer
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra and Trigonometry
Algebra and Trigonometry
Trigonometry
ISBN:
9781938168376
Author:
Jay Abramson
Publisher:
OpenStax
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning