# Working with intersecting polar grids

Geographic Information Systems## How do you solve for Polar intersections?

To find the points of intersection of these polar curves, we’ll **set them equal to each other and solve for θ**. To find the values of r that are associated with these values of θ, we’ll plug the θ values back into either of the original polar curves; we’ll choose r = sin θ r=\sin{\theta} r=sinθ.

## How do you solve intersecting graphs?

When the graphs of y = f(x) and y = g(x) intersect , both graphs have exactly the same x and y values. So we can find the point or points of intersection by **solving the equation f(x) = g(x)**. The solution of this equation will give us the x value(s) of the point(s) of intersection.

## How do you find the intersection of two polar graphs?

Quote from video: *If you have one equation in terms of R and the other in terms of R squared. You'll have to manipulate one or the other so that they're both R squared or they're both just R.*

## How do you do two pairs of polar coordinates?

**If n = 2, then θ = 360° + 45° = 405°, etc.** **Since 0° ≤ θ < 360, therefore the value of θ is 45° and 225°**. The two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360° are (3√2, 45°) and (3√2, 225°).

## What is the formula for intersection?

Point of intersection means the point at which two lines intersect. These two lines are represented by the equation **a _{1}x + b_{1}y + c_{1}= 0** and a

_{2}x + b

_{2}y + c

_{2}= 0, respectively.

## How do you multiply two polars together?

Subtraction is similar. To multiply complex numbers in polar form, **multiply the magnitudes and add the angles**. To divide, divide the magnitudes and subtract one angle from the other.

## What are the theorem on intersecting lines?

**If two lines intersect, then exactly one plane contains both lines** (Theorem 3). If a point lies outside a line, then exactly one plane contains both the line and the point (Theorem 2). If two lines intersect, then they intersect in exactly one point (Theorem 1).

## How many solutions does a graph with intersecting lines have?

one solution

Recall that intersecting lines have **one solution** and therefore the system is consistent. Because the lines are not the same, the equations are independent.

## How do you find missing variables with intersecting lines?

Quote from video: *Now to solve for x i have 10x. Minus 10 equals 180 i'll add 10 to both sides. And i get 10x equals 190 divide by 10 divide by 10 x equals 19..*

## How do you solve a polar plot?

Rules for Drawing Polar Plots

**Find the starting magnitude and the phase of G(jω)H(jω) by substituting ω=0**. So, the polar plot starts with this magnitude and the phase angle. Find the ending magnitude and the phase of G(jω)H(jω) by substituting ω=∞. So, the polar plot ends with this magnitude and the phase angle.

## What is the formula for polar form?

Polar Form Equation

θ=tan^{–}^{1}(y/x)+180° for x<0 .

## How do you find the polar equation?

Solution: Identify the type of polar equation The polar equation is in the form of a limaçon, **r = a – b cos θ**. Since the equation passes the test for symmetry to the polar axis, we only need to evaluate the equation over the interval [0, π] and then reflect the graph about the polar axis.

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