Graph the sets of points whose polar coordinates satisfy the

NompsypeFeplk 2021-11-19 Answered
Graph the sets of points whose polar coordinates satisfy the given polar equation.
The given polar equation is written as follows:
\(\displaystyle-{\frac{{\pi}}{{{4}}}}\le\theta\le{\frac{{\pi}}{{{4}}}},-{1}\le{r}\le{1}\)

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Expert Answer

Zachary Pickett
Answered 2021-11-20 Author has 8745 answers

Consider the polar coordinates as \(\displaystyle{P}{\left({r},\theta\right)}.\)
Here, r is the directed distance from origin O to point Pand \(\theta\) is the directed angle from initial ray to OP.
From the given equation, the value of \(\theta\) varies from \(\displaystyle-{\frac{{\pi}}{{{2}}}}\) to \(\displaystyle{\frac{{\pi}}{{{2}}}}\) and r varies from 1 to 2.
Polar point traces a circle when r is fixed at constant value and it traces a straight line when \(\theta\) is fixed at constant value.
From the analysis, draw the sets of points whose polar coordinates satisfy the given polar equation as shown in
Figure 1.
image

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