# Trigonometric Functions To Maximize Canal Output: 769620

Questions:

Complete the table. The area when  is 10o has been given to help you verify your expressions for columns b and c. Show all
calculations.
MATH 113 PRECALCULUS II Dr. Kowski
2
Angle  Smaller base
of trapezoid
a
Larger base
of trapezoid
b
Height of
trapezoid
c
Area
c
a b

 

2
10o 8 feet 22.1 sq. ft.
20o 8 feet
30o 8 feet
40o 8 feet
50o 8 feet
60o 8 feet
70o 8 feet
80o 8 feet
90o 8 feet
b. Write a general equation for the area as a function of .
MATH 113 PRECALCULUS II Dr. Kowski
3
c. Use your graphing calculator to view a graph of the area function from part b. Also, view the table on your calculator. Hand-sketch the graph of the area function [0, 180] x [0, 90]. Be sure to label axes increments or points AND label the axes according to the problem content.
Provide exact coordinates for any intercepts.
MATH 113 PRECALCULUS II Dr. Kowski 4
d. TRACE on your graphing calculator, what angle  provides the maximum area?
e. Using TABLE on your calculator, what is the maximum area and what angle  provides this maximum area?
f. Do you get different answers for parts d and e above? Explain why or why not.

Part a

 Angle Smaller base of trapezoid a Larger base of trapezoid b Height of Trapezoid c Area: c*((a+b)/2) 10 8 23.75692405 1.389185421 22.1 20 8 23.03508193 1.389185421 21.6 30 8 21.85640646 1.389185421 20.7 40 8 20.25671109 1.389185421 19.6 50 8 18.28460175 1.389185421 18.3 60 8 16 1.389185421 16.7 70 8 13.47232229 1.389185421 14.9 80 8 10.77837084 1.389185421 13.0 90 8 8 1.389185421 11.1

Part b

Part c

Part d

X-axis value with the biggest y-axis value)

Part e

X-axis value with the biggest y-axis value)

Part f

Answers are different.  The graph provides more  values than the table.