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Paraphin [41]
3 years ago
15

(-3, 0) to polar form.

Mathematics
1 answer:
spayn [35]3 years ago
4 0

9514 1404 393

Answer:

  (3; 180°)

Step-by-step explanation:

The point (-3, 0) is located on the -x axis at a distance of 3 units from the origin. The -x axis is at an angle of 180° CCW from the +x axis. So, the polar coordinates are ...

  r = 3

  θ = 180°

This might be written as ...

  (r; θ) = (3; 180°) = (3; π radians)

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\large\underline{\sf{Solution-}}

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\rm :\longmapsto\:\dfrac{sin\theta }{1 + cos\theta }

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\rm \:  =  \: \dfrac{sin\theta }{1 + cos\theta }  \times \dfrac{1 - cos\theta }{1 - cos\theta }

We know,

\purple{\rm :\longmapsto\:\boxed{\tt{ (x + y)(x - y) =  {x}^{2} -  {y}^{2} \: }}}

So, using this, we get

\rm \:  =  \: \dfrac{sin\theta (1  -  cos\theta )}{1 -  {cos}^{2}\theta  }

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\purple{\rm :\longmapsto\:\boxed{\tt{  {sin}^{2}x +  {cos}^{2}x = 1}}}

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\rm \:  =  \: \dfrac{sin\theta (1 -  cos\theta )}{{sin}^{2}\theta  }

\rm \:  =  \: \dfrac{1 - cos\theta }{sin\theta }

<u>Hence, </u>

\\ \red{\rm\implies \:\boxed{\tt{ \rm \:\dfrac{sin\theta }{1 + cos\theta }   =  \: \dfrac{1 - cos\theta }{sin\theta } }}} \\

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