Question

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

Answer 1

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

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

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

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