Question

Find all polar coordinates of point P = (2, 14Á).

Answer 1

Explanation:

Answer 2

Answer with explanation:

The coordinate of point P =(2,14)

Coordinates of point (x,y) in polar form can be represented as

=(r cos A, r sin A)

Where, r is distance from Origin.And , A is angle made by line with positive direction of X axis.

So, writing the given point in polar form:

2= r cos A------------(1)

14= r sin A---------(2)

Squaring 1 and 2 and adding

⇒ 2²+14²=(rcos A)²+(r sin A)²

→4+196=r²(cos²A+sin²A)

→200=r²

→r=10√2 units

Dividing equation 2 by equation 1

`(\sin A)/(\cos A)=(14)/(2)\\\\\tan A=7\\\\A=\tan^(-1)7`

`\tan A=\frac{\text{Perpendicular}}{\text{Base}}=(7)/(1)\\\\\text{Perpendicular}=7\\\\\text{Base}=1\\\\(\text{Hypotenuse})^2=(\text{Perpendicular})^2+(\text{Base})^2\\\\\text{Hypotenuse}=√(7^2+1^2)\\\\=√(50)\\\\\sin A=(7)/(√(50))\\\\\cos A=(1)/(√(50))\\\\\text{So},2=10√(2)*(1)/(√(50))\\\\14=10√(2)*(7)/(√(50))\\\\(2,14)=(10√(2)*(1)/(√(50)),10√(2)*(7)/(√(50)))`