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Perimeter of Hypocycloid given Chord Length Formula

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GoPerimeter of Hypocycloid given Area Formula

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Perimeter of Hypocycloid is the total length of all the boundary edges of the Hypocycloid. Check FAQs

P = \frac{4 \cdot l c}{\sin (\frac{π}{N Cusps})} \cdot \frac{N Cusps - 1}{N Cusps}

P - Perimeter of Hypocycloid?l_c - Chord Length of Hypocycloid?N_Cusps - Number of Cusps of Hypocycloid?π - Archimedes' constant?

Perimeter of Hypocycloid given Chord Length Example

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Here is how the Perimeter of Hypocycloid given Chord Length equation looks like with Values.

Here is how the Perimeter of Hypocycloid given Chord Length equation looks like with Units.

Here is how the Perimeter of Hypocycloid given Chord Length equation looks like.

65.33 = \frac{4 \cdot 12}{\sin (\frac{3.1416}{5})} \cdot \frac{5 - 1}{5}

65.33m = \frac{4 \cdot 12m}{\sin (\frac{3.1416}{5})} \cdot \frac{5 - 1}{5}

65.33 = \frac{4 \cdot 12}{\sin (\frac{3.1416}{5})} \cdot \frac{5 - 1}{5}

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Perimeter of Hypocycloid given Chord Length Solution

Follow our step by step solution on how to calculate Perimeter of Hypocycloid given Chord Length?

FIRST Step Consider the formula

P = \frac{4 \cdot l c}{\sin (\frac{π}{N Cusps})} \cdot \frac{N Cusps - 1}{N Cusps}

Next Step Substitute values of Variables

∴

P = \frac{4 \cdot 12m}{\sin (\frac{π}{5})} \cdot \frac{5 - 1}{5}

Next Step Substitute values of Constants

∴

P = \frac{4 \cdot 12m}{\sin (\frac{3.1416}{5})} \cdot \frac{5 - 1}{5}

Next Step Prepare to Evaluate

∴

P = \frac{4 \cdot 12}{\sin (\frac{3.1416}{5})} \cdot \frac{5 - 1}{5}

Next Step Evaluate

∴

P = 65.3299820814367m

LAST Step Rounding Answer

∴

P = 65.33m

Perimeter of Hypocycloid given Chord Length Formula Elements

Variables

Constants

Functions

Perimeter of Hypocycloid

Perimeter of Hypocycloid is the total length of all the boundary edges of the Hypocycloid.

Symbol: P

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Perimeter of Hypocycloid

Chord Length of Hypocycloid

Chord Length of Hypocycloid is the linear distance between any two adjacent cusps of the Hypocycloid.

Symbol: l_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Chord Length of Hypocycloid

Number of Cusps of Hypocycloid

Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid.

Symbol: N_Cusps

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Cusps of Hypocycloid

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

Other Formulas to find Perimeter of Hypocycloid

Go Perimeter of Hypocycloid

P = \frac{8 \cdot r Large \cdot (N Cusps - 1)}{N Cusps}

Go Perimeter of Hypocycloid given Area

P = 8 \cdot \sqrt{\frac{A \cdot (N Cusps - 1)}{π \cdot (N Cusps - 2)}}

How to Evaluate Perimeter of Hypocycloid given Chord Length?

Perimeter of Hypocycloid given Chord Length evaluator uses Perimeter of Hypocycloid = (4*Chord Length of Hypocycloid)/(sin(pi/Number of Cusps of Hypocycloid))*(Number of Cusps of Hypocycloid-1)/Number of Cusps of Hypocycloid to evaluate the Perimeter of Hypocycloid, Perimeter of Hypocycloid given Chord Length is defined as the total length of all the boundary edges of the Hypocycloid, and calculated using the chord length of the Hypocycloid. Perimeter of Hypocycloid is denoted by P symbol.

How to evaluate Perimeter of Hypocycloid given Chord Length using this online evaluator? To use this online evaluator for Perimeter of Hypocycloid given Chord Length, enter Chord Length of Hypocycloid (l_c) & Number of Cusps of Hypocycloid (N_Cusps) and hit the calculate button.

FAQs on Perimeter of Hypocycloid given Chord Length

What is the formula to find Perimeter of Hypocycloid given Chord Length?

The formula of Perimeter of Hypocycloid given Chord Length is expressed as Perimeter of Hypocycloid = (4*Chord Length of Hypocycloid)/(sin(pi/Number of Cusps of Hypocycloid))*(Number of Cusps of Hypocycloid-1)/Number of Cusps of Hypocycloid. Here is an example- 65.32998 = (4*12)/(sin(pi/5))*(5-1)/5.

How to calculate Perimeter of Hypocycloid given Chord Length?

With Chord Length of Hypocycloid (l_c) & Number of Cusps of Hypocycloid (N_Cusps) we can find Perimeter of Hypocycloid given Chord Length using the formula - Perimeter of Hypocycloid = (4*Chord Length of Hypocycloid)/(sin(pi/Number of Cusps of Hypocycloid))*(Number of Cusps of Hypocycloid-1)/Number of Cusps of Hypocycloid. This formula also uses Archimedes' constant and Sine (sin) function(s).

What are the other ways to Calculate Perimeter of Hypocycloid?

Here are the different ways to Calculate Perimeter of Hypocycloid-

Perimeter of Hypocycloid=(8*Larger Radius of Hypocycloid*(Number of Cusps of Hypocycloid-1))/Number of Cusps of Hypocycloid
Perimeter of Hypocycloid=8*sqrt((Area of Hypocycloid*(Number of Cusps of Hypocycloid-1))/(pi*(Number of Cusps of Hypocycloid-2)))

Can the Perimeter of Hypocycloid given Chord Length be negative?

No, the Perimeter of Hypocycloid given Chord Length, measured in Length cannot be negative.

Which unit is used to measure Perimeter of Hypocycloid given Chord Length?

Perimeter of Hypocycloid given Chord Length is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Perimeter of Hypocycloid given Chord Length can be measured.

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Perimeter of Hypocycloid given Chord Length Formula

​GoPerimeter of Hypocycloid Formula

​GoPerimeter of Hypocycloid given Area Formula

Perimeter of Hypocycloid given Chord Length Example

Perimeter of Hypocycloid given Chord Length Solution

Perimeter of Hypocycloid given Chord Length Formula Elements

Other Formulas to find Perimeter of Hypocycloid

How to Evaluate Perimeter of Hypocycloid given Chord Length?

FAQs on Perimeter of Hypocycloid given Chord Length

Variable Name

GoPerimeter of Hypocycloid Formula

GoPerimeter of Hypocycloid given Area Formula