Question

The polar coordinates of C (pcos,psin). What is p here​

Answer 1

SOLUTION

GIVEN

The polar coordinates of C (pcosθ , psinθ )

TO DETERMINE

The value of p

EVALUATION

Concept Building :

Let O be a fixed point . OX and OY are fixed lines. A point . Let P(x, y) be a point in cartesian coordinate system

If r = Distance of from O and θ be the angular distance of P from OX then the polar coordinates of P is denoted by (r, θ)

If (x, y) be a point in cartesian coordinate system then x = r cosθ and y = r sinθ

r is known as the radius vector and θ is the vectorial angle . Vectorial angle is generally measured in anticlockwise direction

Calculation :

Here the given point is C (pcosθ , psinθ )

The point is in Polar coordinate system

Now

$\sf \: OC = \sqrt{ {(p \cos \theta - 0)}^{2} + {(p \sin \theta - 0)}^{2} }$

$\sf \implies \: OC = \sqrt{ {(p \cos \theta )}^{2} + {(p \sin \theta )}^{2} }$

$\sf \implies \: OC = \sqrt{ {p}^{2} {\cos }^{2}\theta + {p}^{2} {\sin}^{2} \theta }$

$\sf \implies \: OC = \sqrt{ {p}^{2} ({\cos }^{2}\theta + {\sin}^{2} \theta })$

$\sf \implies \: OC = \sqrt{ {p}^{2} }$

$\sf \implies \: OC = p$

From above we can conclude that

p = Distance of from C from origin

FINAL ANSWER

p = Distance of from C from origin

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