Chapter 8 Parametric Equations - Year 2 Flashcards
What are the 2 methods to calculate the domain and range of parametric equations (in cartesian forms)
The domain of f is the range of x=
The range of f is th3 range of y=
So use graphs
Think about limits
How do you find a cartesian form of parametric equations?
(Simple way)
Make 1 parametric equation in terms of t then sub it into the other
What does cartesian equation mean?
What impact does this have?
An equation in terms of y and x
Unless specified you don’t need to give the answer in the form y=f(x)
How do you plot parametric equations?
Draw a table and then plot them like polar coordinates
What is the general method to solve where parametric equations intercept anything?
You need to find the t value
Why may a question give you a graph?
It wants you to see that an event will happen when it cuts the x axis
What is a harder way to find cartesian equations from parametric equations?
You can use trig identities. Eg x=sinx y=cosx, as sinx^2+cosx^2=1 x^2+y^2=1
What is the method to find where a parametric equation reaches its maximum
Differentiation
Why may a domain of t>0 may be unrealistic?
It will happen forever
How do you determine how long until the next cycle will start?
You look at the period of the graphs
Then you choose the biggest one (round the answer unless specified)
What is the period of cos?
2π
What is the period of sinx
2π
What is the period of sin^2 -sinx?
Explain why?
The period of sin^2 is π but the period of sinx is 2π. You need to pick the bigger one
