To convert y=3x+4 to polar form, you can use the following steps:
Cartesian coordinates, also known as rectangular coordinates, use the x-axis and y-axis to locate a point on a plane. Polar coordinates, on the other hand, use the distance from the origin (r) and the angle from the positive x-axis (θ) to locate a point on a plane. In polar coordinates, a point is represented as (r, θ) instead of (x, y).
No, only linear equations with the form y = mx + b can be converted to polar form. This is because polar coordinates are based on the distance from the origin and the angle from the positive x-axis, which are not directly related to the slope (m) and y-intercept (b) of a linear equation.
Converting an equation to polar form can be useful for solving problems involving circular or rotational motion, such as finding the position of an object at a specific angle or distance from a fixed point. It can also make certain calculations and graphing easier, depending on the situation.
Yes, polar coordinates can be converted to Cartesian coordinates using the following equations:
x = rcosθ
y = rsinθ
In other words, the x-coordinate is equal to the radius multiplied by the cosine of the angle, and the y-coordinate is equal to the radius multiplied by the sine of the angle.