I with the following questions.

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Discussion Overview

The discussion revolves around solving mathematical problems related to trigonometric functions and optimization of a rectangle's area, including specific equations and methods for finding solutions. The scope includes theoretical reasoning, mathematical problem-solving, and application of calculus concepts.

Discussion Character

  • Mathematical reasoning
  • Homework-related
  • Debate/contested

Main Points Raised

  • Some participants inquire about the definition of csc and suggest using a calculator for solving trigonometric equations.
  • One participant proposes dividing the equations to simplify the process of finding solutions for sin and cos.
  • Another participant mentions using guess and check to find dimensions of a rectangle, while others argue that calculus methods should be employed instead.
  • There are suggestions to express the area of the rectangle in terms of one variable and to maximize it using calculus techniques.
  • Some participants provide specific values for the dimensions of the rectangle, while others question the correctness of these values and emphasize the need for a systematic approach.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate methods for solving the problems, particularly regarding the use of calculus versus simpler techniques. There is no consensus on the best approach or the correctness of specific answers provided.

Contextual Notes

Some participants reference prior knowledge from earlier coursework, indicating that the problems may not require advanced calculus techniques, which adds to the uncertainty about the necessary methods for solving the problems.

Who May Find This Useful

Students studying trigonometry and optimization, particularly those in high school mathematics courses, may find this discussion relevant for understanding different approaches to solving similar problems.

DLxX
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1. Given csc(-) = 1.4, what is one possible value of (-) in radians?

2. Solve for (-) in each equation. Give the exact value if possible. The domain is the set of all real numbers.

a) 2sin(3theta)=1 b) 2sin(-) cos(-) =sin(-)

(-) = theta btw

3. A rectange has a length of x and width of y. If 3x + 2y = 96, find the largest area the rectange can have and the dimensions of the largest rectange.
 
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3.It's rectangle (sic).Do you know how to use Lagrange multipliers...?

2 & 1.Post your work.

Daniel.
 
For 3 write the area in terms of x.
How do you maximize a function of one variable?
 
For number 3 I ended up getting x as 16 and y as 24, using guess and check. Is this correct?
 
U can't use guess and check.U need to use CALCULUS...


Daniel.
 
It may be the correct answer but it'd be better to learn a method, or a reason.

The above hints were one way. here's another.


you want to maximize xy subject to 3x+2y=96

that's the same as maximizing 2r*3s, letting 2r=x and 3y=s, subject to

r+s=16, which by symmetry always happens when r=s=8 so x=16 and y=24 indeed.
 
1. How is csc defined? After you have answered that, use a calculator.

2. a) Divide both sides of the equation by 2: sin(3θ)= 1/2 You should be able to write 3θ immediately - if not use a calculator.
b) An obvious possibility is sin(θ)= 0. If sin(θ) is not 0, you can divide the equation by sin(θ) to get 2cos(θ)= 1 so cos(θ)= 1/2 .
Now see part (a)!

3. The area of a rectangle with sides x and y is A= xy. You are told 3x+ 2y= 96 so
y= 48- (3/2)x. A= x(48- (3/2)x)= 48x- (3/2)x2. You can now complete the square to find the largest possible value of that.
 
dextercioby said:
U can't use guess and check.U need to use CALCULUS...


Daniel.
I'm in Grade 12 Pre Calculus and this assignment isn't based on new material, but material most likely learned in Grade 11 Pre Calculus, so I doubt I have to use Calculus. Unless the Calculus needed is very basic.
 
HallsofIvy said:
1. How is csc defined? After you have answered that, use a calculator.

2. a) Divide both sides of the equation by 2: sin(3?)= 1/2 You should be able to write 3? immediately - if not use a calculator.
b) An obvious possibility is sin(?)= 0. If sin(?) is not 0, you can divide the equation by sin(?) to get 2cos(?)= 1 so cos(?)= 1/2 .
Now see part (a)!

3. The area of a rectangle with sides x and y is A= xy. You are told 3x+ 2y= 96 so
y= 48- (3/2)x. A= x(48- (3/2)x)= 48x- (3/2)x2. You can now complete the square to find the largest possible value of that.

For number 2a) I got 9.6 and 170.4 degrees. and for 2b) I got 60 and 300 degrees. Is this correct?
 

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