:) transform each polar equation in rectangular coordinates and identify its shape. 1. theta= 1.34 radians 2. r=tan(theta)sec(theta)

To solve this question we will make use of the basic relationship between the variables of the polar and cartesian coordinates.

They are:

and and

Let us solve the question now:

1.

The above is the answer for question 1. It is a straight line which passes through the origin.

2. It is given that:

which can be rewritten as:

Now, we know that:

Therefore, we get:

Which gives us, after cross multiplying :

(Since, )

Therefore, is the final answer we get by cross multiplying x.

This is a parabola.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2