Consider the point on the polar graph below. A. Represent the point's location in the polar form (r,θ) where 0≤r≤5 and −2π≤θ<0.
(r,θ)=

B. Represent the point's location in the polar form (r,θ) where 0≤r≤5 and 0≤θ<2π.
(r,θ)=

C. Represent the point's location in the polar form (r,θ) where −5≤r≤0 and −2π≤θ<0.
(r,θ)=

​

a) We can clearly see that the radius is r = 5, now let's find the angle.

We can see that it lies between the angles (2/3)*pi and (5/6)*pi

which one is the angle in between these two?

We can calculate it as:

θ = ( (2/3)*pi + (5/6)*pi)/2 = pi*( 4/6 + 5/6)/2 = pi*(9/6)/2 = pi*(9/12) = pi*(3/4)

But we want to write this in the range:

−2π≤θ<0

Knowing that we have a period of 2*pi

our angle will be equivalent to:

pi*(3/4) - 2*pi = pi*( 3/4 - 2) = pi*(3/4 - 8/4) = pi*(-5/4)

Then this point can be  represented as:

(5, (-5/4)*pi)

B) Same as before, but this time we have 0≤θ<2π

The first value of θ that we found is in that range, so this will be:

(5, (3/4)*pi)

C) Here we have −5≤r≤0 and −2π ≤ θ< 0.

For point a, we already know that:

θ = (-5/4)*pi

But the radius part looks tricky, right?

In the standard notation, the variable r (radius) is defined as:

r = IrI

This means that we always use r as a positive number, and if in the notation we write a negative number, then when we work with that we just change the sign.

This means that having r = -5 is exactly the same as r = 5.

Then we can write this point as:

(-5, (-5/4)*pi)

answer: i guess 5 units?

step-by-step explanation:

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!