Question

Can someone help with this

Answer 1

In rectangular coordinates, the point
`\((2, \pi/3)\)` is equivalent to
`\((1, √(3))\)`.

To plot the point
`\((2, \pi/3)\)` and convert it to rectangular coordinates, we first need to understand that
`\((r, \theta)\)` represents a point in polar coordinates, where r is the distance from the origin and
`\(\theta\)` is the angle with the positive x-axis.

Here, r = 2 and
`\(\theta = \pi/3\)`. To convert these polar coordinates to rectangular coordinates (x, y), we can use the formulas:

`\[ x = r \cos(\theta) \]`

`\[ y = r \sin(\theta) \]`

In this case:

`\[ x = 2 \cos\left((\pi)/(3)\right) \]`

`\[ y = 2 \sin\left((\pi)/(3)\right) \]`

Now, compute the values:

`\[ x = 2 \cdot (1)/(2) = 1 \]`

`\[ y = 2 \cdot (√(3))/(2) = √(3) \]`

So, in rectangular coordinates, the point
`\((2, \pi/3)\)` is equivalent to
`\((1, √(3))\)`. To plot this point, locate it at x = 1 on the x-axis and
`\(y = √(3)\)` on the y-axis.