Chapter 9: Q. 1 (page 629)

In Problems 1–3, plot each point given in polar coordinates, and find its rectangular coordinates:
$(3, \frac{π}{6})$

Short Answer

Expert verified

The rectangular co-ordinates of the polar co-ordinate $(3, \frac{π}{6})$ are $(\frac{3 \sqrt{3}}{2}, \frac{3}{2})$ and the graph is

Step by step solution

Step 1. Given Information

We are given the polar co-ordinates as $(3, \frac{π}{6})$

Comparing it with standard polar co-ordinates $(r, θ)$ , we get,

$r = 3 θ = \frac{π}{6}$

Step 2. Plotting the polar co-ordinate

Since the angle is $\frac{π}{6}$ , we will make the angle between the axis and the line as $\frac{π}{6}$ . Also the length is given as $r = 3$

Therefore, the graph will look like,

Step 3. Rectangular co-ordinates.

We know, the relation between polar and rectangular co-ordinates is,

$x = r \cos θ and y = r \sin θ$

Thus, the value of

x = 3 \cdot \cos \frac{π}{6} = \frac{3 \sqrt{3}}{2}

The value of $y = r \sin θ = 3 \cdot \sin \frac{π}{6} = \frac{3}{2}$

The co-ordinate will be $(\frac{3 \sqrt{3}}{2}, \frac{3}{2})$

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In Problems 1–3, plot each point given in polar coordinates, and find its rectangular coordinates:
$(3, \frac{π}{6})$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Plotting the polar co-ordinate

Step 3. Rectangular co-ordinates.

One App. One Place for Learning.

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In Problems 1–3, plot each point given in polar coordinates, and find its rectangular coordinates:3,π6

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Plotting the polar co-ordinate

Step 3. Rectangular co-ordinates.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Statistics

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 1–3, plot each point given in polar coordinates, and find its rectangular coordinates:
$(3, \frac{π}{6})$