Concept explainers
To determine: The equations for the lines that are tangent to the cardioids at the points where it crosses the x -axis.
Answer to Problem 25RE
The required equations are
Explanation of Solution
Given information:
The equation of the four-petaled rose:
Formula used:
Product rule of differentiation:
Calculation:
The given equation is
The equation shows that the tips of petals are at the points where r is maximum.
Also, the maximum value of sine is 1.
So,
The above are the points where
It is seen that in polar
Rewrite the coordinates as:
Here, the polar curves lie in the xy -plane. This means the slope of the polar curve and the sloe of the tangent line are same.
So,
For
For
For
For
Hence, the required equations are
Chapter 11 Solutions
Calculus: Graphical, Numerical, Algebraic
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