I with the following questions.

  • Thread starter DLxX
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In summary, the conversation involved solving for possible values of a given equation and finding the largest area of a rectangle. The value of csc was defined and a calculator was used to find the values of theta in the given equations. The method of completing the square was also mentioned to find the largest possible value of the area. One person suggested using calculus, but the other person pointed out that the material is typically learned in pre-calculus and may not require calculus. The possible values obtained for the equations were 9.6 and 170.4 degrees for 2a) and 60 and 300 degrees for 2b).
  • #1
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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  • #2
3.It's rectangle (sic).Do you know how to use Lagrange multipliers...?

2 & 1.Post your work.

Daniel.
 
  • #3
For 3 write the area in terms of x.
How do you maximize a function of one variable?
 
  • #4
For number 3 I ended up getting x as 16 and y as 24, using guess and check. Is this correct?
 
  • #5
U can't use guess and check.U need to use CALCULUS...


Daniel.
 
  • #6
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.
 
  • #7
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.
 
  • #8
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.
 
  • #9
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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