Answer:
The correct answer is C. [tex](0,10)[/tex].
Step-by-step explanation:
The polar coordinates are defined in terms of r and θ, where r is the distance of the point from the origin and θ is the angle made with the positive x-axis.
To convert from Polar Coordinates (r, θ) to Cartesian Coordinates (x, y) apply the following conversion formulas:
[tex]x = r\cos \theta \\y = r\sin \theta[/tex]
We know that [tex]r=10[/tex] and [tex]\theta = 0.5\pi[/tex]
So, the cartesian coordinates are,
[tex]x=10\cos \left(0.5\pi \right)=10\cos \left(\frac{1}{2}\pi \right)=10\cos \left(\frac{\pi }{2}\right)\\\\\mathrm{Use\:the\:following\:trivial\:identity}:\quad \cos \left(\frac{\pi }{2}\right)=0\\\\x=10\cdot \:0\\x=10[/tex]
[tex]y=10\sin \left(0.5\pi \right)=10\sin \left(\frac{1}{2}\pi \right)=10\sin \left(\frac{\pi }{2}\right)\\\\\mathrm{Use\:the\:following\:trivial\:identity}:\quad \sin \left(\frac{\pi }{2}\right)=1\\\\y= 10[/tex]
The correct answer is C. [tex](0,10)[/tex].
