Chapter Sections 8.1-8.3 Flashcards
What are polar coordinates?
P (r, theta)
r is the radius
Theta is the angle it is on in the unit circle
What are two equations to know for converting from polar to rectangular?
r sin (theta) =y r cos (theta) =x
When converting from rectangular to polar what do you do?
First you use the Pythagorean theorem to find the radius
Then use tangent to find the degree
To write an equation in rectangular coordinate what are your two options
- multiply both sides by r
- square both sides
What is the equation for limaçon curves without an inner loop? And how do you know it is a limaçon curve without inner loop?
R=a+/- b cos theta
You know it is a limaçon curve without inner loop because a > b
How many times does a limaçon curve without an inner loop pass through the origin?
It doesn’t pass through the origin
What is the equation for a limaçon curve with an inner loop? And how do you know it is this type of curve?
R=a +/- b sin theta
You know it’s this equation because a
How many times does a limaçon curve with inner loop cross the origin?
Twice
What is the equation for a cardiod graph (there are two)?
How do you know it’s a cardiod graph?
R=a +/- a sin theta
R=a +/- a cos theta
You know it’s this graph because a will = b
Cos is the value for y or x
For x
Sin is the value for y or x
For y
What makes something rectangular?
What makes something polar
When it has to do with x and y and i
When it has to do with theta and radius
What is the general equation for a complex number?
A + bi
When plotting a complex number where is the imaginary number with the i and where is the real number?
Imaginary number with i goes on y axis and real number goes with x axis
What is the polar form of a complex number?
Z= r (cos theta + i sin theta)
What is the equation for products of complex numbers
z1 * z2= r1*r2 (cos (theta1+theta2) + i sin(theta1+theta2))
What is the equation for the quotient of complex numbers?
z1/z2= r1/r2 (cos (theta1-theta2) + i sin(theta1-theta2))
What is the equation for a complex number to a certain power
Z^n=r^n (cos(n*theta) + i sin(n *theta))
What is the equation for finding complex roots?
Zk=the Nth square root of r (cos(theta/n +360k/n) + i sin(theta/n + 360k/n))
What would K be in the equation for finding the complex roots
K = n-1
For example)
If n is 3 then k would be 0,1,2 giving us three solutions
What is known for the complex root of unity?
Unity means 1
So r = 1
Theta= 0 degrees
What is the trick you can do when finding roots of unity
For each possible equation you can simply keep adding the number in front of the K. So if it is 90k then in the solutions it would be cos 0 the in the next possible solution it would be cos 90 etc
REMEMBER!!!
If graphing state whether it is a circle (with its center and radius), if it is a vertical line, slanted line, or horizontal line.
What are the points to test for a limaçon curve using sine in the equation such as 2-4sin
3pi/2 5pi/3 11pi/6 0 Pi/6 Pi/3 Pi/2
What are the points to test for a limaçon curve using cos in its equation
0 Pi/6 Pi/3 Pi/2 2pi/3 5pi/6 Pi
