Q. 30 The arc length of polar function... [FREE SOLUTION]

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Chapter 9: Q. 30 (page 775)

The arc length of polar functions: Find the arc lengths of the following polar functions. $r = c s c 胃 for 胃鈭� [\frac{鈭� 蟺}{6}, \frac{蟺}{6}]$

Short Answer

Expert verified

The arc length is $2 units$

Step by step solution

Given information

The curve is $r = c s c 胃 for 胃鈭� [\frac{鈭� 蟺}{6}, \frac{蟺}{6}]$

Arc length

The arc length of the curve is given by,

$L = {鈭�}_{伪}^{尾} \sqrt{r^{2} + {(\frac{d r}{d 胃})}^{2}} d 胃 L = {鈭�}_{\frac{蟺}{4}}^{\frac{3 蟺}{4}} \sqrt{{(c s c 胃)}^{2} + {(- c s c 胃 c o t 胃)}^{2}} d 胃 [鈭� \frac{d r}{d 胃} = - c s c 胃 c o t 胃] L = {鈭�}_{\frac{蟺}{4}}^{\frac{3 蟺}{4}} \sqrt{c s c^{2} 胃 - c s c^{2} 胃 c o t^{2} 胃} d 胃 L = {鈭�}_{\frac{蟺}{4}}^{\frac{3 蟺}{4}} \sqrt{c s c^{2} 胃 (1 - c o t^{2} 胃)} d 胃 L = {鈭�}_{\frac{蟺}{4}}^{\frac{3 蟺}{4}} \sqrt{c s c^{2} 胃 (c s c^{2} 胃)} d 胃 [1 - c o t^{2} 胃 = c s c^{2} 胃] L = {鈭�}_{\frac{蟺}{4}}^{\frac{3 蟺}{4}} c s c^{2} 胃 d 胃 L = {[- c o t 胃]}_{\frac{蟺}{4}}^{\frac{3 蟺}{4}} L = [- c o t \frac{3 蟺}{4} + c o t (\frac{蟺}{4})] L = [1 + 1] L = [2] L = 2 units$

The arc length is $2 units$

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91影视

The arc length of polar functions: Find the arc lengths of the following polar functions. $r = c s c 胃 for 胃鈭� [\frac{鈭� 蟺}{6}, \frac{蟺}{6}]$

Short Answer

Step by step solution

Given information

Arc length

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91影视

The arc length of polar functions: Find the arc lengths of the following polar functions. r=csc胃for胃鈭�鈭�蟺6,蟺6

Short Answer

Step by step solution

Given information

Arc length

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Probability and Statistics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

The arc length of polar functions: Find the arc lengths of the following polar functions. $r = c s c 胃 for 胃鈭� [\frac{鈭� 蟺}{6}, \frac{蟺}{6}]$