s3w2 Precalc FC Polar coordinates

Review: y=5 represents a

y=5 represents a

x=3 represents a

x=3 represents a

What does a negative theta mean?

What does a negative r mean?

A relation is considered a function when there is only one output for ever input. for y=x^2, which is the input and which is the output?

The typical convention we use is that y is a function of x. We have seen that these can be invertible, so x can be a function of y. similarly the convention for polar function is that r is a function of theta. There are probably occasions where these are invertible, but I don't think they will come up much. For now, I want you to think of r being a function of theta. that means that

Consider what the "vertical line test" means for determining if a relationship is a function in a cartesian graph. What kind of test would you use to determine if a graph in a polar coordinate is a function?

graphing a circle using cartesian coordinates, you would use

Where a is a constant, and the radius of the circle. In polar coordinates, you would use r=a, where a is that same constant. One of these equations is a function, the other is not. Explain why.

Consider the following polar graph.

The graph overlaps itself several times. In a cartesian coordinate system you would know this is not a function, but in polar coordinates it is. The equation for this graph

Your friend tells you that there are multiple outputs for the same input, therefore it is not a function. How do you respond?

Which of the following explains how to transform a cartesian ordered pair into a polar coordinate ordered pair

which of the following shows how to convert a polar ordered pair to a cartesian ordered pair?

the graph of x=y gives a straight line, and has a domain of all real numbers, and a range of all real numbers. What would the equation

look like, and what would its domain and range look like?

Jane finds a graph of what she assumes is y=x with a domain of x\ge 0 . She then realized she is looking at a polar graph. What is the polar equation of that graph?

the relationship between x,y and r,theta is always the same, whether you are converting points, or working with equations. match the relationships here.

intuitively, what do you think a polar equation like

will look like when you turn it into a rectangular equation?

to work with going from polar to rectangular, you need to be comfortable substituting in the following two relations

and

so if I give you the equation

what would you get by substituting (don't solve for y yet)

now, if you did that right, you should be taking the sine of an arc tan function. lets separate that one out first. and let's simplify, to see how it works. lets just solve

One of the trickier parts of precalc is that you stare at it trying all sorts of different algebraically, but a shift in perspective is probably better. try instead thinking through this one geometrically. which of the following shows what

gives you.

What is the hypotenuse of the triangle above?

given just that information, which of the following is

if you noticed, the original equation has

which of the following is the proper translation of that?

go to this desmos graph. https://www.desmos.com/calculator/hjrbagaejm

play with different values of a,b,c and d. How would you describe the translation and dilation transformations are for polar equations?

Categorize the basic concepts from this lesson into "I've got this", "I'm shaky" and "so confused