
2021 Unit 6 Review
Flashcard
•
Mathematics
•
11th - 12th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the distance formula in a coordinate plane?
Back
The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).
2.
FLASHCARD QUESTION
Front
How do you convert rectangular coordinates to polar coordinates?
Back
To convert from rectangular coordinates \((x, y)\) to polar coordinates \((r, \theta)\): 1. Calculate \(r = \sqrt{x^2 + y^2}\). 2. Calculate \(\theta = \tan^{-1}(\frac{y}{x})\).
3.
FLASHCARD QUESTION
Front
What is a polar equation?
Back
A polar equation expresses a relationship between the radius \(r\) and the angle \(\theta\) in polar coordinates.
4.
FLASHCARD QUESTION
Front
What is the general form of a polar equation?
Back
The general form of a polar equation can be expressed as \(r = f(\theta)\), where \(f(\theta)\) is a function of \(\theta\).
5.
FLASHCARD QUESTION
Front
What is the significance of the angle in polar coordinates?
Back
The angle \(\theta\) in polar coordinates indicates the direction of the point from the origin.
6.
FLASHCARD QUESTION
Front
What is a limacon in polar coordinates?
Back
A limacon is a type of polar graph that can have an inner loop, and is represented by equations of the form \(r = a + b \sin(\theta)\) or \(r = a + b \cos(\theta)\).
7.
FLASHCARD QUESTION
Front
What does the equation \(r = 6 + 6 \sin(\theta)\) represent?
Back
This equation represents a limacon with an inner loop.
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