Polar Coordinates

[ponkyhong]

I totally don't understand (b) and (c). Can you guys provide me steps if you guys know how to do?

 

[stapel]

When you say that you "totally don't understand", does this mean that you are needing a lesson on polar coordinates first? Or something else? Please be specific. Thank you!

 

[ponkyhong]

What are the answers to (b) and (c), and can you guys provide me steps? I know I have to use some formulas, but I just don't know how to relate them with this question. Should I use r=k theta? And what is the next step? Thanks. Much appreciated! I have a test on polar coordinates soon and I could't contact my teacher :/

 

[Quaid]

What are the answers to (b) and (c), and can you guys provide me steps?

From the summary page of the posting guidelines (i.e., Read Before Posting info), we find the following statement.

"We do not generally post immediate answers or step-by-step solutions to assignments."

Volunteers at this site do not have time for typing up lessons or teaching classroom material.

Should I use r=k theta? And what is the next step?

I have a test on polar coordinates soon

You're familiar with the function r(θ) = kθ, where k is a Real number

(Your precalculus class ought to have studied graphs of this function.)

When k is positive, the function generates a spiral graph (using polar coordinates) that is similar to the two that you posted.

In your exercise 6(b), the graph indicates that the value of r(θ) is Pi/4, for some value of θ.

Tell us, what is θ, at that point along the spiral?

You can answer this in your head, from understanding the polar-coordinate system. Answering this question is the first step.

Once you understand the value of θ at that point, you may find the polar equation for that graph by substituting the known values for θ and r(θ) into the function definition, followed by solving for k.

Cheers :cool:

PS: If you missed the lesson in class, you may find several by googling: "polar equation" spiral lessons graphs

 

[ponkyhong]

What do you mean by r(theta) = k(theta)? I'm only familiar with r= k theta/ r = theta. theta is 45 degree at that point I guess? I'm sorry I still don't get it.:sad:

 

[stapel]

What do you mean by r(theta) = k(theta)?

Are you not familiar with function notation (such as the left-hand side, where "r" is a function of the angle-measure "theta")? Are you not familiar with variable multiplication (such as the right-hand side, where the variable "theta" is multiplied by the constant "k")?

 

[Quaid]

What do you mean by r(theta) = k(theta)?

That is a simple function statement. As Stapel wrote, the notation with parentheses next to the letter r is called Function Notation.

The name of the function is r.

θ is the name of the function's input. In other words, symbol θ represents the independent variable.

r(θ) is the output of function r. In other words, symbol r(θ) represents the dependent variable.

The product of k and θ is the definition (or "rule") for function r. In other words, kθ tells us what function r does with its input. (It multiplies the input by k and outputs that product.)

I'm only familiar with r= k theta/ r = theta.

You need to be careful, when texting mathematics. What you typed above (highlighted in red) means this:

$\displaystyle r = k \cdot \dfrac{\theta}{r} = \theta$

I'm sure you did not intend to write that.

r = kθ expresses the same relationship as r(θ)=kθ

It's just a different notation; calculus is all about the study of function behavior. We need to use function notation, when working with functions in calculus.

theta is 45 degree at that point I guess?

That's not correct; one revolution occurs when θ equals 2Pi radians.

Are you guessing because you have been away from math courses for awhile? I suggested earlier that you google for basic lessons. Did you look for lessons about polar equations?

You posted on the calculus board. I'm not sure why you're working this exercise (it's not calculus), but, if it's part of a placement exam for enrolling in a calculus course, you should skip the questions which you do not understand. If it's review of prerequisite material, then you have a lot of catching up to do. You should consider taking a precalculus course (or intensive self-review) before trying to learn calculus.

We're sorry, but volunteers at this site do not have time to teach classroom material. (Thousands of lessons already exist, on the Internet.)

Topics such as polar equations, radian measure, and function notation require weeks of instruction and practice. You can do self-review of algebra, trigonometry, and precalculus topics online at the Khan Academy. (Google them.) Their short video lessons are well organized by topic.

I wish you good fortune, in your future studies! If you see or hear something in lessons or examples that you do not understand, please start a new thread and ask a specific question about it.

Cheers :cool: