Convert the rectangular coordinates (sqrt(3), 0) into polar form. Express the angle...

1. Identify the rectangular coordinates: The given rectangular coordinates are $(x, y) = (\sqrt{3}, 0)$.
2. Calculate the radial distance (r): The formula for the radial distance $r$ in polar coordinates is $r = \sqrt{x^2 + y^2}$. Substituting the given values:
$$r = \sqrt{(\sqrt{3})^2 + (0)^2}$$ $$r = \sqrt{3 + 0}$$ $$r = \sqrt{3}$$
Since we need a positive value of $r$, $r = \sqrt{3}$ is the correct value.
3. Calculate the angle (theta): The formula for the angle $\theta$ in polar coordinates is $\tan(\theta) = \frac{y}{x}$. Substituting the given values:
$$\tan(\theta) = \frac{0}{\sqrt{3}}$$
$$\tan(\theta) = 0$$
To find $\theta$, we take the arctangent of 0. The general solution for $\tan(\theta) = 0$ is $\theta = n\pi$, where $n$ is an integer.
4. Determine the correct angle within the interval: We are given the interval $0 \leq \theta < 2\pi$. We also need to consider the quadrant of the point $(\sqrt{3}, 0)$. Since $x = \sqrt{3}$ (positive) and $y = 0$, the point lies on the positive x-axis.
For $\theta = n\pi$:
If $n=0$, $\theta = 0\pi = 0$. This is within the interval $0 \leq \theta < 2\pi$ and corresponds to the positive x-axis.
If $n=1$, $\theta = 1\pi = \pi$. This is within the interval $0 \leq \theta < 2\pi$ but corresponds to the negative x-axis.
If $n=2$, $\theta = 2\pi$. This is not within the interval $0 \leq \theta < 2\pi$.
Since the point $(\sqrt{3}, 0)$ is on the positive x-axis, the correct angle is $\theta = 0$.
5. Write the polar form: The polar form of a point is given by $(r, \theta)$. Using the calculated values, the polar form is $(\sqrt{3}, 0)$.