What is the Cartesian form of $(24, \frac{15 π}{6}))$ $(24,(15pi)/6))$ ?

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What is the Cartesian form of $(24, \frac{15 π}{6}))$ $(24,(15pi)/6))$ ?

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Answer 1 · 2015-12-28T20:37:26

The Cartesian form of $(24, \frac{15 π}{6})$ $(24,(15pi)/6)$ is $(0, 24) .$ $(0,24).$

Explanation:

Consider the figure. In this figure the angle is 22.6 but in our case enter image source here

Let the Cartesian form of $(24, \frac{15 π}{6})$ $(24,(15pi)/6)$ be $(x, y) .$ $(x,y).$
Consider the figure. From figure:

$cos (\frac{15 π}{6}) = \frac{x}{24}$ $Cos((15pi)/6)=x/24$

$\Rightarrow x = 24 cos (\frac{15 π}{6}) = 24 (0) = 0$ $impliesx=24Cos((15pi)/6) =24(0)=0$
$\Rightarrow x = 0$ $impliesx=0$
Also from figure:

$sin (\frac{15 π}{6}) = \frac{y}{24}$ $Sin((15pi)/6)=y/24$
$\Rightarrow y = 24 sin (\frac{15 π}{6}) = 24 (1) = 24$ $impliesy=24Sin((15pi)/6)=24(1)=24$
$\Rightarrow y = 24$ $implies y=24$

Therefore the Cartesian form of $(24, \frac{15 π}{6})$ $(24,(15pi)/6)$ is $(0, 24) .$ $(0,24).$

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What is the Cartesian form of $(24, \frac{15 π}{6}))$ $(24,(15pi)/6))$ ?

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