Which is the standard form of the equation with p = 26, O=3pi/4 ?
the O before the =3pi has a diagonal slash through it.
To determine the standard form of the equation with p = 26 and O = 3π/4, it is necessary to understand the context or topic that the equation represents. As provided in the question, it seems like these are variables representing polar coordinates. The variable "p" typically represents the radial distance from the origin to a point, and the variable "θ" (with the diagonal slash) represents the angle measured counterclockwise from the positive x-axis.
So, the given information implies that we have a point in polar coordinates with a radial distance of 26 and an angle of 3π/4 (which is 135 degrees) from the positive x-axis.
Now, let's convert this polar point to rectangular or Cartesian coordinates, which are represented by the variables "x" and "y." The conversion formulas are as follows:
x = p * cos(θ)
y = p * sin(θ)
By substituting the given values, we find:
x = 26 * cos(3π/4)
y = 26 * sin(3π/4)
Since cos(3π/4) = sin(3π/4) = sqrt(2)/2, we can simplify the equations to:
x = 26 * (sqrt(2)/2) = 13 * sqrt(2)
y = 26 * (sqrt(2)/2) = 13 * sqrt(2)
Therefore, the standard form of the equation would be:
(x, y) = (13 * sqrt(2), 13 * sqrt(2))