For Exercises 77-78, determine whether the statement is true or false for two points P r 1 , θ 1 and Q r 2 , θ 2 represented in polar coordinates. If the statement is false, give a counterexample. If θ 1 = θ 2 then P and Q are the same distance from the pole.
For Exercises 77-78, determine whether the statement is true or false for two points P r 1 , θ 1 and Q r 2 , θ 2 represented in polar coordinates. If the statement is false, give a counterexample. If θ 1 = θ 2 then P and Q are the same distance from the pole.
Solution Summary: The author analyzes whether the statement, "If left|theta '_1'right' is true or false. The angle depends on both magnitude and direction.
For Exercises 77-78, determine whether the statement is true or false for two points
P
r
1
,
θ
1
and
Q
r
2
,
θ
2
represented in polar coordinates. If the statement is false, give a counterexample.
If
θ
1
=
θ
2
then P and Q are the same distance from the pole.
Points z1 and z2 are shown on the graph.z1 is at (4 real,6 imaginary), z2 is at (-5 real, 2 imaginary)Part A: Identify the points in standard form and find the distance between them.Part B: Give the complex conjugate of z2 and explain how to find it geometrically.Part C: Find z2 − z1 geometrically and explain your steps.
A polar curve is represented by the equation r1 = 7 + 4cos θ.Part A: What type of limaçon is this curve? Justify your answer using the constants in the equation.Part B: Is the curve symmetrical to the polar axis or the line θ = pi/2 Justify your answer algebraically.Part C: What are the two main differences between the graphs of r1 = 7 + 4cos θ and r2 = 4 + 4cos θ?
A curve, described by x2 + y2 + 8x = 0, has a point A at (−4, 4) on the curve.Part A: What are the polar coordinates of A? Give an exact answer.Part B: What is the polar form of the equation? What type of polar curve is this?Part C: What is the directed distance when Ø = 5pi/6 Give an exact answer.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Polar Coordinates Basic Introduction, Conversion to Rectangular, How to Plot Points, Negative R Valu; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=aSdaT62ndYE;License: Standard YouTube License, CC-BY