Chapter 9: Q. 16 (page 730)

Find all values of $a$ and $b$ such that $(a, b)$ represents the same point whether it is given in rectangular coordinates or polar coordinates.

Short Answer

Expert verified

The required point is $(0, 0)$ .

Step by step solution

Given information

The point $(a, b)$ .

Calculation

Consider the point $(a, b)$ .

The objective is to find a point which is same in polar coordinate system and rectangular coordinate system.

The point which is same in polar coordinate system and rectangular coordinate system is $(0, 0)$ .

Now suppose $(0, 0)$ is a point in rectangular system.

In the coordinate (0,0), x=0 and y=0.

To find the value of $r$ use the equation $r = \sqrt{x^{2} + y^{2}}$ .

Then,

r = \sqrt{(0)^{2} + (0)^{2}} [since x = 0, y = 0] r = \sqrt{0} r = 0

To calculate $θ$ use the formula $θ = \tan^{- 1} (\frac{y}{x})$ .

Then

θ = \tan^{- 1} (\frac{0}{0}) [since x = 0, y = 0] θ = \tan^{- 1} (0) θ = 0 [since \tan 2 π = \tan π = 0]

Then $(r, θ) = (0, 0)$ .

Thus, the coordinate $(0, 0)$ is same in polar coordinate system and rectangular coordinate system.

Therefore, the required point is $(0, 0) .$

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Find all values of $a$ and $b$ such that $(a, b)$ represents the same point whether it is given in rectangular coordinates or polar coordinates.

Short Answer

Step by step solution

Given information

Calculation

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Find all values of aand bsuch that (a,b) represents the same point whether it is given in rectangular coordinates or polar coordinates.

Short Answer

Step by step solution

Given information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Study anywhere. Anytime. Across all devices.

Find all values of $a$ and $b$ such that $(a, b)$ represents the same point whether it is given in rectangular coordinates or polar coordinates.