# I need help with the following questions.

1. Mar 8, 2005

### DLxX

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.

2. Mar 8, 2005

### dextercioby

3.It's rectangle (sic).Do you know how to use Lagrange multipliers...?

Daniel.

3. Mar 8, 2005

### Euclid

For 3 write the area in terms of x.
How do you maximize a function of one variable?

4. Mar 9, 2005

### DLxX

For number 3 I ended up getting x as 16 and y as 24, using guess and check. Is this correct?

5. Mar 9, 2005

### dextercioby

U can't use guess and check.U need to use CALCULUS...

Daniel.

6. Mar 9, 2005

### matt grime

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. Mar 9, 2005

### HallsofIvy

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&theta;)= 1/2 You should be able to write 3&theta; immediately - if not use a calculator.
b) An obvious possibility is sin(&theta;)= 0. If sin(&theta;) is not 0, you can divide the equation by sin(&theta;) to get 2cos(&theta;)= 1 so cos(&theta;)= 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. Mar 9, 2005

### DLxX

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. Mar 13, 2005

### DLxX

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