Graph the sets of points whose polar coordinates satisfy the

vousetmoiec 2021-11-23 Answered
Graph the sets of points whose polar coordinates satisfy the given polar equation.
The given polar equation is written as follows:
$$\displaystyle{\frac{{\pi}}{{{4}}}}\le\theta\le{\frac{{{3}\pi}}{{{4}}}},{0}\le{r}\le{1}$$

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Expert Answer

William Yazzie
Answered 2021-11-24 Author has 291 answers

Consider the polar coordinates as P(r, 0).
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 $$\displaystyle{\frac{{\pi}}{{{4}}}}\to{\frac{{{3}\pi}}{{{4}}}}$$ and r varies from 0 to 1.
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.

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