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
[tex]\frac{\sin A}{\cos A}=\frac{14}{2}\\\\\tan A=7\\\\A=\tan^{-1}7[/tex]
[tex]\tan A=\frac{\text{Perpendicular}}{\text{Base}}=\frac{7}{1}\\\\\text{Perpendicular}=7\\\\\text{Base}=1\\\\(\text{Hypotenuse})^2=(\text{Perpendicular})^2+(\text{Base})^2\\\\\text{Hypotenuse}=\sqrt{7^2+1^2}\\\\=\sqrt{50}\\\\\sin A=\frac{7}{\sqrt{50}}\\\\\cos A=\frac{1}{\sqrt{50}}\\\\\text{So},2=10\sqrt{2}*\frac{1}{\sqrt{50}}\\\\14=10\sqrt{2}*\frac{7}{\sqrt{50}}\\\\(2,14)=(10\sqrt{2}*\frac{1}{\sqrt{50}},10\sqrt{2}*\frac{7}{\sqrt{50}})[/tex]
