Find all points of interception of the pair of polar equations in polar form r=3 and r=-4cosx

Question
Equations
asked 2020-12-15
Find all points of interception of the pair of polar equations in polar form r=3 and \(\displaystyle{r}=-{4}{\cos{{x}}}\)

Answers (1)

2020-12-16
Step 1
Given polar equations:
r=3
\(\displaystyle{r}=-{4}{\cos{{\left({0}\right)}}}\)
Step 2
To find points of intersection of given polar equations:
\(\displaystyle-{4}{\cos{{\left({0}\right)}}}={3}\)
\(\displaystyle{\cos{{\left({0}\right)}}}=-\frac{{3}}{{4}}\)
\(\displaystyle{0}={{\cos}^{{-{1}}}{\left(-\frac{{3}}{{4}}\right)}}\)
\(\displaystyle{0}={138.6}^{{\circ}},{221.4}^{{\circ}}\)
Step 3
Therefore,
The points of intersection of the pair of polar equations are
\(\displaystyle{\left({3},{138.6}^{{\circ}}\right)}\)
\(\displaystyle{\left({3},{221.4}^{{\circ}}\right)}\)
0

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