Question

Which equation is the Gizmo using to find the x coordinates​

Answer 1

Answer:

The correct answer is C. $(0,10)$.

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:

                                                      $x = r\cos \theta \\y = r\sin \theta$

We know that $r=10$ and $\theta = 0.5\pi$

So, the cartesian coordinates are,

$x=10\cos \left(0.5\pi \right)=10\cos \left(\frac{1}{2}\pi \right)=10\cos \left(\frac{\pi }{2}\right)\\\\\mathrm{Use\:the\:following\:trivial\:identity}:\quad \cos \left(\frac{\pi }{2}\right)=0\\\\x=10\cdot \:0\\x=10$

$y=10\sin \left(0.5\pi \right)=10\sin \left(\frac{1}{2}\pi \right)=10\sin \left(\frac{\pi }{2}\right)\\\\\mathrm{Use\:the\:following\:trivial\:identity}:\quad \sin \left(\frac{\pi }{2}\right)=1\\\\y= 10$

The correct answer is C. $(0,10)$.